J.P. Wellisch CERN/EP/SFT

J.P. Wellisch, CERN/EP/SFT

Physics of Hadronic Showers at LHC

HEP 2003, Europhysics conference, Aachen, Germany.

J.P. WellischCERN/EP/SFT


OverviewOverview

Introducing a system for Introducing a system for classification of modeling classification of modeling approaches.approaches.

Two novel theoretical approaches:Two novel theoretical approaches: Chiral invariant phase-space decayChiral invariant phase-space decay Binary cascadeBinary cascade

SummarySummary


Three categories of Three categories of modeling approachesmodeling approaches

Data driven modelingData driven modeling Parametrization driven modelingParametrization driven modeling Theory driven modelingTheory driven modeling


Parameterisation driven Parameterisation driven modelsmodels

Total cross-sections.Total cross-sections. Final state generators - two domains:Final state generators - two domains:

high energy inelastic (Aachen, CMS)high energy inelastic (Aachen, CMS) low energy inelastic, elastic, fission, capture (TRIUMF, UBC, low energy inelastic, elastic, fission, capture (TRIUMF, UBC,

CERN)CERN) Stopping particlesStopping particles

base line (TRIUMF, CHAOS)base line (TRIUMF, CHAOS) mu- (TRIUMF, FIDUNA)mu- (TRIUMF, FIDUNA) pi- (INFN, CERN, TRIUMF) pi- (INFN, CERN, TRIUMF) K- (Crystal Barrel, TRIUMF)K- (Crystal Barrel, TRIUMF) anti-protons (JLAB, CERN)anti-protons (JLAB, CERN) Electromagnetic transitions of the exotic atom prior to capture; Electromagnetic transitions of the exotic atom prior to capture;

effects of atomic binding. (Novosibirsk, ESA)effects of atomic binding. (Novosibirsk, ESA)


Example:Example:Proton Proton cross-sectionscross-sections


Data driven models: Data driven models:

Radioactive decay, photon evaporation, internal Radioactive decay, photon evaporation, internal conversion (conversion (ENSDF)ENSDF), elastic scattering (SAID), etc.., elastic scattering (SAID), etc..

Low energy neutron Low energy neutron Based on evaluated data: G4NDN, derived fromBased on evaluated data: G4NDN, derived from

ENDF, Jef, JENDL, CENDL, ENSDF, Brond, IRDF, ENDF, Jef, JENDL, CENDL, ENSDF, Brond, IRDF, FENDL, MENDL,...FENDL, MENDL,...

Sampling codes for ENDF-B VI derived data formatsSampling codes for ENDF-B VI derived data formats Use the file-system to ensure granular and Use the file-system to ensure granular and

transparent access/usage of data setstransparent access/usage of data sets Doppler broadening not static on input data, but on Doppler broadening not static on input data, but on

the fly from 0K data.the fly from 0K data.


Example of data driven Example of data driven modeling: neutron capture, modeling: neutron capture, and and isotope productionisotope production


Theory driven modelsTheory driven models Ultra-high energy modelsUltra-high energy models

Parton transport model (in discussion)Parton transport model (in discussion) High energy modelsHigh energy models

‘‘Fritjof’ type string model (CERN)Fritjof’ type string model (CERN) Quark gluon String (CERN)Quark gluon String (CERN) Pythia(7) interface (Lund, CERN)Pythia(7) interface (Lund, CERN)

Intra-nuclear transport models (or replacements)Intra-nuclear transport models (or replacements) Bertini cascade (HIP, CERN)Bertini cascade (HIP, CERN) Binary cascades (CERN, U.Frankfurt)Binary cascades (CERN, U.Frankfurt) QMD (CERN, Inst.Th.Phys. Frankfurt)QMD (CERN, Inst.Th.Phys. Frankfurt) Chiral invariant phase-space decay (JLAB, CERN, ITEP)Chiral invariant phase-space decay (JLAB, CERN, ITEP) Partial Mars rewrite (Kyoto, in collaboration with UVic. and FNAL)Partial Mars rewrite (Kyoto, in collaboration with UVic. and FNAL)

De-excitationDe-excitation Evaporation, fission, multi-fragmentation, fermi-break-up (Valencia)Evaporation, fission, multi-fragmentation, fermi-break-up (Valencia)


Example of a theoretical Example of a theoretical final state generator: final state generator: quark gluon string modelquark gluon string model


Novel theoretical Novel theoretical approachesapproaches

Chiral invariant phase-space decayChiral invariant phase-space decay A quark level 3-dimensional event A quark level 3-dimensional event

generator for fragmentation of generator for fragmentation of excited hadronic systems (quasmons) excited hadronic systems (quasmons) into hadrons.into hadrons.

Binary cascadeBinary cascade In between Bertini’s cascade and In between Bertini’s cascade and

quantuum molecular dynamics.quantuum molecular dynamics.


Binary cascadingBinary cascading

Some characteristics of binary cascading: Some characteristics of binary cascading: In binary cascading, like in QMD, each nucleon participant In binary cascading, like in QMD, each nucleon participant

is described byis described by

And the total wave function is assumed to be the direct And the total wave function is assumed to be the direct product of these (no antisymmetrization). product of these (no antisymmetrization).

The equations of motion for this wave-form are identical in The equations of motion for this wave-form are identical in structure to the classical Hamilton equations, and can be structure to the classical Hamilton equations, and can be solved by numerical integration.solved by numerical integration.

Nuclear Hamiltonian is calculated from optical potentials Nuclear Hamiltonian is calculated from optical potentials based on the information on all hadrons in the systembased on the information on all hadrons in the system

))())((/2exp())/(2(),,,( 24/3 xtiptqxLLtpqx iiii


The imaginary part of the The imaginary part of the G-matrix G-matrix

Acts like a scattering termActs like a scattering term Described as 2-body, point-like collisionsDescribed as 2-body, point-like collisions

Collision assumption of black disk cross-Collision assumption of black disk cross-sectionsection


The nuclear modelThe nuclear model The nuclear density distributions used are the The nuclear density distributions used are the

Saxon-Woods form for high ASaxon-Woods form for high A

And the harmonic oscillator form for light nuclei And the harmonic oscillator form for light nuclei (A<17)(A<17)

The nucleon momenta are randomly selected The nucleon momenta are randomly selected between zero and the Fermi momentum at a between zero and the Fermi momentum at a chosen location in configuration space.chosen location in configuration space.

]/)exp[(1)( 0

aRrr

ii

)/exp()()( 2'22/32' RrRr ii


Why binary cascade?Why binary cascade? The name binary cascade comes from the The name binary cascade comes from the

fact that only binary collisions (and decay) fact that only binary collisions (and decay) are considered, likeare considered, like

No further details on the mathematics, but No further details on the mathematics, but the nucleon and delta resonances taken the nucleon and delta resonances taken into consideration are theseinto consideration are these

17750*

21901232 pKorNpp


Binary cascadeBinary cascadepredictionprediction

Sample the Impact parameter overA large area.Make the ratio of ‘hits’ To trials, times the area sampled


Forward peaks in proton Forward peaks in proton scattering (256 MeV)scattering (256 MeV)

Beryllium

Aluminum

Iron

Lead


Chiral Invariant Phase-space Chiral Invariant Phase-space Decay.Decay.

A quark level 3-dimensional event generator for A quark level 3-dimensional event generator for fragmentation of excited hadronic systems fragmentation of excited hadronic systems (quasmons) into hadrons.(quasmons) into hadrons.

Based on the QCD idea of asymptotic freedomBased on the QCD idea of asymptotic freedom Local chiral invariance restoration lets us consider Local chiral invariance restoration lets us consider

quark partons massless, and we can integrate the quark partons massless, and we can integrate the invariant phase-space distribution of quark partons invariant phase-space distribution of quark partons and quark exchange (fusion) mechanism of and quark exchange (fusion) mechanism of hadronizationhadronization

The only non-kinematical concept used is that of a The only non-kinematical concept used is that of a temperature of the quasmon.temperature of the quasmon.


Vacuum CHIPSVacuum CHIPS This allows to calculate the decay of free excited This allows to calculate the decay of free excited

hadronic systems:hadronic systems: In an finite thermalized system of N partons with In an finite thermalized system of N partons with

total mass M, the invariant phase-space integral is total mass M, the invariant phase-space integral is proportional to , and the statistical density proportional to , and the statistical density of states is proportional to . Hence we can of states is proportional to . Hence we can write the probability to find N partons with write the probability to find N partons with temperature T in a state with mass M as temperature T in a state with mass M as

Note that for this distribution, the mean mass Note that for this distribution, the mean mass square is square is

42 NMTMe /

dMeMdW TMN /42

22 )22(2 TNNM


Vacuum CHIPSVacuum CHIPS

We use this formula to calculate the We use this formula to calculate the number of partons in the quasmon, and number of partons in the quasmon, and obtain the parton spectrum obtain the parton spectrum

To obtain the probability for quark To obtain the probability for quark fusion into hadrons, we can compute fusion into hadrons, we can compute the probability to find two partons with the probability to find two partons with momenta q and k with the invariant momenta q and k with the invariant mass mass ..

32

1

N

M

k

kdk

dW

cos21

)cos1(2

21

21),,( 2

4

qdqdMk

kq

MkM

qMkP

N


Vacuum CHIPSVacuum CHIPS Using the delta function to perform the integration Using the delta function to perform the integration

and the mass constraint, we find the total and the mass constraint, we find the total kinematical probability of hadronization of a parton kinematical probability of hadronization of a parton with momentum k into a hadron with mass with momentum k into a hadron with mass

Accounting for spin and quark content of the final Accounting for spin and quark content of the final state hadron adds (2s+1) and a combinatorial factor.state hadron adds (2s+1) and a combinatorial factor.

At this level of the language, CHIPS can be applied to At this level of the language, CHIPS can be applied to p-pbar annihilationp-pbar annihilation

32 21)3(4

2

N

kMNk

kM


Anti proton annihilationAnti proton annihilation


Anti proton annihilationAnti proton annihilation


Nuclear CHIPSNuclear CHIPS In order to apply CHIPS for an excited hadronic In order to apply CHIPS for an excited hadronic

system within nuclei, we have to add parton system within nuclei, we have to add parton exchange with nuclear clusters to the modelexchange with nuclear clusters to the model

The kinematical picture is, that a color neutral The kinematical picture is, that a color neutral quasmon emits a parton, which is absorbed by quasmon emits a parton, which is absorbed by a nucleon or a nuclear cluster. This results in a a nucleon or a nuclear cluster. This results in a colored residual quasmon, and a colored colored residual quasmon, and a colored compound.compound.

The colored compound then decays into an The colored compound then decays into an outgoing nuclear fragment and a ‘recoil’ quark outgoing nuclear fragment and a ‘recoil’ quark that is incorporated by the colored quasmon.that is incorporated by the colored quasmon.


The parton exchange The parton exchange diagramdiagram


A few results: For more A few results: For more information see:information see: Eur.Phys.Journal A9,411(2000) andEur.Phys.Journal A9,411(2000) and Eur.Phys.Journal A9,421(2000) Eur.Phys.Journal A9,421(2000)


ConclusionsConclusions Established UML and OO design as Established UML and OO design as

technique for pooling expertise.technique for pooling expertise. Established categorization of physics Established categorization of physics

modeling.modeling. Binary cascade has significant predictive Binary cascade has significant predictive

power, also in the giant resonance regime, power, also in the giant resonance regime, providing an alternative for the ‘classical’ providing an alternative for the ‘classical’ cascade models.cascade models.

Chiral invariant phase-space decay allows to Chiral invariant phase-space decay allows to use partonic concepts at energies far below use partonic concepts at energies far below 1 GeV.1 GeV.

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J.P. Wellisch CERN/EP/SFT