String Parton Models in Geant4

GunterGunter Folger, Folger,Johannes-Peter WellischJohannes-Peter Wellisch

CERN EP/SFTCERN EP/SFT

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

String Parton ModelsString Parton Models• Models for inelastic interactions of Models for inelastic interactions of

primary hadrons with nucleiprimary hadrons with nuclei• for particles of high incident for particles of high incident

energiesenergies• Models split intoModels split into

• String excitationString excitation• String fragmentationString fragmentation

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

String Parton ModelsString Parton Models• Two models for string excitationTwo models for string excitation

• FTFModel, a diffractive scattering modelFTFModel, a diffractive scattering model• Quark Gluon String ModelQuark Gluon String Model

• String fragmentation common, butString fragmentation common, but• fragmentation function specific for string fragmentation function specific for string

modelmodel

• Secondaries passed on to lower energy Secondaries passed on to lower energy models models

• Nucleus passed to models for Nucleus passed to models for fragmentation, deexcitation, ...fragmentation, deexcitation, ...

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

Applicability of modelsApplicability of models• QGS QGS Model Model

• Incident energies above 5-20 GeV up to Incident energies above 5-20 GeV up to 50 TeV50 TeV

• Incident particles: pion, Kaon, proton, Incident particles: pion, Kaon, proton, neutron, and gammaneutron, and gamma

• FTF ModelFTF Model• Energies as aboveEnergies as above• Incident particles: all (longlived) hadronsIncident particles: all (longlived) hadrons

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

DesignDesign

• G4vstringmodelG4vstringmodel

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

Quark gluon string model Quark gluon string model (QGSM)(QGSM)

• The algorithmThe algorithm• A 3-dimensional nuclear model is built upA 3-dimensional nuclear model is built up• It is collapsed into 2 dimensionsIt is collapsed into 2 dimensions• The impact parameter is calculatedThe impact parameter is calculated• Hadron-nucleon collision probabilities Hadron-nucleon collision probabilities

calculation based on eiconal model, using calculation based on eiconal model, using Gaussian density distributions for hadrons Gaussian density distributions for hadrons and nucleons.and nucleons.

• Sampling of the number of pomerons Sampling of the number of pomerons exchanged in each collisionexchanged in each collision

• Unitarity cut, string formation and decay.Unitarity cut, string formation and decay.

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

The nuclear model The nuclear model (shared)(shared)

• The nuclear density distributions used are the The nuclear density distributions used are the Saxon-Woods form for high A (Grypeos 1991)Saxon-Woods form for high A (Grypeos 1991)

• And the harmonic oscillator form for light And the harmonic oscillator form for light nuclei (A<17, Elton 1961)nuclei (A<17, Elton 1961)

• The nucleon momenta are randomly chosen The nucleon momenta are randomly chosen between zero and the fermi momentumbetween zero and the fermi momentum

]/)exp[(1)( 0

aRrr

ii

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

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

The nuclear model, cont.The nuclear model, cont.• The sampling is done in a The sampling is done in a

correlated manner correlated manner • such the local phase-space densities such the local phase-space densities

stay within what is allowed by Pauli’s stay within what is allowed by Pauli’s principle, and principle, and

• such that the sum of all nucleon such that the sum of all nucleon momenta equals zero.momenta equals zero.

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

QGSM Model – Collision QGSM Model – Collision criterioncriterion

• In the Regee Gribov approach, the In the Regee Gribov approach, the collision probability can be written ascollision probability can be written as

• wherewhere

• AndAnd

• (Capella 1978)(Capella 1978)

1

)( ),()]),(2exp[1(/1),(n

ijn

ijijijij sbpsbucsbp

!)],(2[

)],(2exp[/1),(2

2)(

nsbu

sbucsbpn

ijijij

nij

))(4/exp(2

)(),( 22 sbszsbu ijij

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

QGSM Model - DiffractionQGSM Model - Diffraction• Diffraction is split off using the Diffraction is split off using the

shower enhancement factor c shower enhancement factor c (Baker 1976).(Baker 1976).

)),(),((1),( sbpsbpccsbp ijijij

totijij

diffij

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

QGSM Model - String QGSM Model - String formationformation

• String formation is done via the String formation is done via the partons exchange (Capella 94, partons exchange (Capella 94, Kaidalov 82) mechanism, sampling Kaidalov 82) mechanism, sampling the parton densities, and ordering the parton densities, and ordering pairs of partons into color coupled pairs of partons into color coupled entities.entities.

n

i

n

iii

hpnn

h xxufxxxxfi

2

1

2

1021221 )1()(),,...,,(

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

QGS model QGS model and K induced reactions and K induced reactions

• Pomeron trajectory and vertex Pomeron trajectory and vertex parameters found in a global fit to parameters found in a global fit to elastic, total and diffractive (6% elastic, total and diffractive (6% assumed) cross-sections for assumed) cross-sections for nucleon, kaon and pion scattering nucleon, kaon and pion scattering off nucleons.off nucleons.

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

QGS Model QGS Model electro nuclear reactions electro nuclear reactions

• Small cross section, gamma Small cross section, gamma interacts with one (random) interacts with one (random) nucleonnucleon

• Using vector dominance modelUsing vector dominance model

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

FTF model FTF model • The algorithmThe algorithm

• Build 3-dimensional nucleusBuild 3-dimensional nucleus• Calculate impact parameters with all nucleonsCalculate impact parameters with all nucleons• Hadron-nucleon collision probabilitiesHadron-nucleon collision probabilities

• using inelastic cross section from eiconal modelusing inelastic cross section from eiconal model• Collision between partons modeled as momentum Collision between partons modeled as momentum

exchangeexchange• Momentum exchange Momentum exchange qq excites hadron and nucleon excites hadron and nucleon• Condition on exited massesCondition on exited masses

• Strings formed from exited particlesStrings formed from exited particles

222tHadron qmm

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

Longitudinal String Longitudinal String FragmentationFragmentation

• AlgorithmAlgorithm• String between constituentsString between constituents• Break string by inserting Break string by inserting q-qbar q-qbar pairpair

• u : d : s : qq = 1 : 1 : 0.27 : 0.1u : d : s : qq = 1 : 1 : 0.27 : 0.1• Break string at pair new string + Break string at pair new string +

hadron hadron • GaussianGaussian P Ptt , <P , <Ptt

22>=0.5 GeV>=0.5 GeV• Split longitudinal momentum using Lund Split longitudinal momentum using Lund

or “QGSM” fragmentation functionsor “QGSM” fragmentation functions

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

K+, scattering off AuK+, scattering off Au

QGSQGS ModelModel

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

Pion and proton scatteringPion and proton scattering

QGSQGS ModelModel

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

FTF FTF ModelModel

• Picture on ave. Picture on ave. multiplicity per multiplicity per particle type for particle type for secondariessecondaries

p H p H X X 200 GeV/c 200 GeV/c

G.Folger,J.P.Wellisch CERN/EP/SFT Geant4 @ Triumf 2003

SummarySummary• Both models are currently under Both models are currently under

validation using testbeam datavalidation using testbeam data• Much help was coming from Much help was coming from

• N.AmelinN.Amelin• A.B.KaidalovA.B.Kaidalov