Monte Carlo 2005, Chattanooga

Parton String Models in Geant4

Gunter Folger,

Johannes-Peter Wellisch

CERN PH/SFT

Contents

Model Overview Object Oriented design Quark Gluon String model Diffractive Scattering model Comparison to experiment

Overview

Two parton string models Diffractive Scattering model Quark Gluon String Model

Final state generators modeling inelastic interactions of primary hadrons with nuclei for primaries of high incident energies

Cross section for reactions not part of final state generator

Parton String Models

Models split into String excitation String hadronization

String hadronization common, fragmentation function specific to string model

Damaged nucleus passed to models for nuclear fragmentation, de-excitation, ...

Applicability of models

QGS Model Incident particles: pion, Kaon, proton, neutron,

and gamma Incident particle energies from O(10 GeV) up to

100 TeV Diffractive Scattering Model

Incident particles: all (long lived) hadrons Energies as above

Object Oriented Design

Quark Gluon String Model

Pomeron exchange model Hadrons exchange one or several Pomerons

Equivalent to color coupling of valence quarks Partons connected by quark gluon strings

Quark gluon string model Algorithm

A 3-dimensional nuclear model is built up Nucleus collapsed into 2 dimensions The impact parameter is calculated Hadron-nucleon collision probabilities

calculation based on quasi-eikonal model, using Gaussian density distributions for hadrons and nucleons.

Sampling of the number of Pomerons exchanged in each collision

Unitarity cut, string formation and decay.

The nuclear model

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

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

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

]/)exp[(1)( 0

aRrr

ii

The nuclear model, cont.

Nucleon momenta are randomly chosen between zero and the Fermi momentum Local density approximation.

The sampling is done in a correlated manner such that the local phase-space densities stay

within what is allowed by Pauli’s principle, and such that the sum of all nucleon momenta

equals zero.

QGS model - Collision criterion

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

where

And

(Capella 1978)

!

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

22)(

n

sbusbucsbp

ni

iini

))(4/exp(2

)(),( 22 sb

szsbu ii

1

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

in

iiii sbpsbucsbp

QGS model - Diffraction

Diffraction is split off using the shower enhancement factor c (Baker 1976).

)),(),((1

),( sbpsbpc

csbp iii

totii

diffi

QGS model - String formation

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

n

i

n

iii

hpnn

h xxufxxxxfi

2

1

2

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

QGS model for and K induced reactions

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

QGS Model for photo nuclear reactions

Photon interacts with nucleons with small photo nuclear cross section

Using vector dominance photon considered as vector meson

Hadron and nucleon exchange momentum Longitudinal momentum exchange excites

hadron and nucleon These independently hadronize into

secondary hadrons

Diffractive String model

Diffractive String model Algorithm Build 3-dimensional nucleus Calculate impact parameters with all

nucleons Hadron-nucleon collision probabilities

using inelastic cross section from eiconal model

Scattering of primary on N nucleons results in N+1 excited strings

Hadronize strings

Longitudinal String Fragmentation

String extends between constituents Break string by inserting parton pair

u : d : s : qq = 1 : 1 : 0.27 : 0.1 Break string at pair new string + hadron Split longitudinal momentum using Lund or

“QGSM” fragmentation functions Gaussian Pt , <Pt

2>=0.9 GeV2

Average multiplicity

per particle type

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

Average Average multiplicitiesmultiplicities

M.Gazdzicki, O.Hansen, Nucl.Phys. A58(1991) 754

enlarged scale

Pion scattering – rapidity distribution pi- Mg pi+ X , Plab 320 GeV/c

Solid dots: J.J.Whitmore et.al., Z.Phys.C62(1994)199

Pion scattering - pt2 distribution pi- Mg pi+ X , 320GeV/c

Solid dots: J.J.Whitmore et.al., Z.Phys.C62(1994)199

Pions from Proton (400GeV/c) scattering off Ta QGSQGS Model - Invariant cross Model - Invariant cross sectionsection

Solid dots:

N.A.Nikiforov et.al.

Phys.Rev.C22(1980) 754

Ekin [GeV]

Ekin [GeV]

Ekin [GeV]

]N

ucle

on

sr

m

b/(G

eV/c

)

GeV

[

dd

333

pAE

70° 90° 118°

137° 160°

Pions from Proton (400GeV/c) scattering off Ta DiffractiveDiffractive Model - Invariant Model - Invariant cross sectioncross section

Solid dots:

N.A.Nikiforov et.al.

Phys.Rev.C22(1980) 754

Ekin [GeV]

Ekin [GeV]

Ekin [GeV]

]N

ucle

on

sr

m

b/(G

eV/c

)

GeV

[

dd

333

pAE

90° 118°

137° 160°

70°

Summary

Geant4 offers choice of physics modeling

Choice of two theory inspired models for high

energy primary hadrons Parameterised models available too

QGS model performs better than diffractive scattering model