Hadronic interactions and EAS

Ralph Engel

Forschungszentrum Karlsruhe, Germany

Outline

Toy model: important parameters of had. interactions

Predictions of interaction models (hadron-air)

Constraints from theory & accelerator data:
- Differences of predictions realistic
- Uncertainty range properly reflected

Air shower predictions:
- Impact on energy and composition measurements
- Detector optimization

Heitler's model of em. showers

Number of particles N(X)

atmospheric depth X (g/cm2)

λ

2n particles after n interactions

Assumption:
shower maximum reached if E(X) = Ec

E0

Primary particle: photon

. . . .

Muon production in had. showers

Primary particle: proton

Only charged pions initiate
new hadronic cascades

π0 decay immediately

Cascade ends with decay at energy Edec

Toy model parameters

Hadronic interaction model

interaction cross section

multiplicity of secondary particles

ratio of neutral to charged pion / kaon multiplicities

Atmosphere as target and calorimeter

critical energy

density: typical pion / kaon decay energy

Number of shower particles proportional to energy

Comparison of energies

Comparison of model predictions

Cosmic ray hadronic interaction models

High energy models:

DPMJET II.5 and III (Ranft / Roesler, RE & Ranft)

neXus 2.0 and 3.0 (Drescher, Hladik, Ostapchenko, Pierog & Werner)

QGSJET 98 and 01 (Kalmykov & Ostapchenko)

SIBYLL 1.7 and 2.1 (Engel / RE, Fletcher, Gaisser, Lipari & Stanev)

Low/intermediate energy models:

GHEISHA (Fesefeldt)

Hillas' splitting algorithm (Hillas)

FLUKA (Fasso, Ferrari, Ranft & Sala)

UrQMD (Bass, Bleicher et al.)

TARGET (RE, Gaisser, Protheroe & Stanev)

HADRIN/NUCRIN (Hänßgen & Ranft)

SOPHIA (Mücke, RE, Rachen, Protheroe, Stanev)

Gribov-Regge type models, minijets

Parametrizations of data

Cross section predictions

Production

cross section h-air:

at least one new particle produced in interaction

(Heck, 2004)

Wide range of predictions:

high energy

pion and kaon cross sections

(Heck, 2004)

Multiplicity predictions

Average secondary particle multiplicity (charged)

Secondary particle multiplicity distribution

(Heck, 2004)

Particle energy distribution

Momentum distribution in CMS

Feynman xF ~ p||/pmax

Elasticity: energy fraction carried by fastest secondary particle

Photons

(Heck, 2004)

pi-14N collisions

Mean depth of shower maximum

(Heck, 2004)

Superposition model:

MC simulation (CORSIKA):

Predictions depend on had. interaction model

Partial compensation of various effects (cross section - inelasticity)

Shower size: Ne-Nμ correlation

Curves: full width at half maximum

Model dependence strongly increasing with energy

Good agreement with superposition model:

(Heck, 2004)

Are the differences between the predictions reasonable?

(i) Description of existing (accelerator) data

(ii) Theoretically sound basis of extrapolation

Cross section calculation (i)

Gribov-Glauber approximation

proton-proton

proton-proton

Cross section calculation (ii)

Reliability test:
proton-carbon data

“Simple” Glauber
calculation

Calculation with

screening corrections

Cross section calculation (iii)

Spread in cross section predictions not in contradiction to data

proton-air cross section

p-anti-p cross section

Cross section calculation (iv)

K+-p cross section

Shortcoming:
pion-air and kaon-air cross sections should agree at low energy

Secondary particle multiplicity

Mean charged particle multiplicity

Proton-antiproton at CERN SPS & Tevatron

Multiplicity distribution

Ecm

(Heck, 2004)

Leading particle production (i)

Elab ~ 4x1011 eV

Fermilab

HERA: p-γ → p/n X

No indications of significant scaling violation of leading particle distributions

Elab ~ 2x1013 eV

Leading particle production (ii)

Extremely inelastic events

Nearly elastic events

p-air → p/n X

Distribution of momentum fraction of leading baryon

Do the different model predictions exhaust the uncertainty range?

There can be only one answer: NO

One counter-example sufficient ...

Parton density saturation (RHIC)?

Low energy:

pronounced leading

particle effect

High energy & central collision:
black disk limit,
no leading particles!!!

Model by Drescher, Dumitru, Strikman,
hep-ph/0408073

Parton density saturation scenarios

proton showers: moderate growth of gluon density

Leading particle distribution:
air shower predictions very sensitive,
extreme case: protons might look like iron!

(Drescher, Dumitru,
Strikman, hep-ph/0408073)

proton showers::
fast growth of gluon density: contradiction to data

SIBYLL (Fe)

SIBYLL (p)

Implications on energy / composition reconstruction

Energy/composition: Ne-Nμ correlation

Curves: full width at half maximum

(Heck, 2004)

No significant reduction of uncertainty
expected without new accelerator data

Further development
and tuning of models
will reduce spread
somewhat

Example: KASCADE composition

QGSJET 01

SIBYLL 2.1

KASCADE: high resolution/precision data, analysis limited by model uncertainties

Energy spectra KASCADE

quality of description of data

(A. Haungs)

QGSJET

SIBYLL

Detector design optimization (i)

- Sea level

- Low-energy
muons

- Single
model

1014 eV

1015 eV

1016 eV

1017 eV

1018 eV

Detector design optimization (ii)

- Mountain
altitude

- Low-energy
muons

- Single
model

1014 eV

1015 eV

1016 eV

1017 eV

1018 eV

Detector design optimization (iii)

- Mountain
altitude

- High-energy
muons

- Single
model

1014 eV

1015 eV

1016 eV

1017 eV

1018 eV

Detector design optimization (vi)

- Sea level

- Low-energy
muons

- Several
models

1014 eV

1015 eV

1016 eV

1017 eV

1018 eV

Detector design optimization (v)

- Mountain
altitude

- Low-energy
muons

- Several
models

1014 eV

1015 eV

1016 eV

1017 eV

1018 eV

- Excellent energy
resolution ~10%

- Virtually no model
dependence

Fluorescence detector: energy (i)

Simulation:

- Ecal: ionization deposit in
atmosphere

- perfect shower profile
measurement assumed

(Karlsruhe Auger Group: Unger, Pierog et al.)

Fluorescence technique at
low energy:

- visible energy correction
strongly composition dependent

- best energy resolution ~15%

Fluorescence detector: energy (ii)

Simulation:

- Nmax: shower size at
maximum (E>1 MeV)

- perfect shower profile
measurement assumed

(Karlsruhe Auger Group: Unger, Pierog et al.)

Fluorescence technique at
low energy:

- visible energy correction
strongly composition dependent

- fluctuations for known
composition stronger

- best energy resolution ~20%

Fluorescence detector: composition (i)

Detailed MC simulation: 10 showers
zenith angle 35°, QGSJET

Fluctuations of shower profile important

Fluorescence detector: composition (ii)

Simulation:

CONEX hybrid simulation code

10,000 showers for each component

model: neXus

E = 1018 eV

Expectation: similar problems and uncertainties
as for Ne-Nμ correlation method

(Karlsruhe Auger Group: Unger, Pierog et al.)

Conclusions & outlook

Model uncertainties in first approximation reasonable

Uncertainties do not exhaust theoretically expected range

No significant improvement without new accelerator data

Ne-Nμ and fluorescence of comparable resolution if

high altitude detector (600 – 700 g/cm2)

low- and high-energy muons are measured simultaneously

Excellent energy resolution of IceTop/IceCube detector possible

Model uncertainties seem impossible to estimate reliably

Need multi-component / hybrid detectors for checking model uncertainties (calorimetry, electrons, muons, Xmax)

Example: HiRes-MIA measurement

MIA: muon density at 600m

Composition iron dominated,
no significant change with energy

HiRes: depth of shower maximum

Composition changes to proton dominated one

Discrimination potential of LHC (i)

p-p collisions at LHC at √s = 14 TeV

major experiments consider to do CR relevant measurements
(for example, CMS / CASTOR / TOTEM)

CMS

CASTOR

TOTEM

Ralph Engel

2004-07-16T09:21:05

Ralph Engel