String Parton Models in Geant4
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Transcript String Parton Models in Geant4
Parton String Models in Geant4
Gunter Folger,
Johannes-Peter Wellisch
CERN PH/SFT
Monte Carlo 2005, Chattanooga
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)
0
(r i )
1 exp[( ri R) / a]
And of the harmonic oscillator form for light
nuclei (A<17, Elton 1961)
(ri ) (R )
' 2 3 / 2
exp( ri / R'2 )
2
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
pi (bi , s) 1 / c(1 exp[ 2u (bi , s)]) pi (bi , s)
where
(n)
n 1
2
n
[
2
u
(
b
,
s
)]
i
pi( n ) (bi , s) 1 / c exp[ 2u (bi2 , s)]
n!
And
z ( s)
u (b , s)
exp(bi2 / 4 ( s))
2
(Capella 1978)
2
i
QGS model - Diffraction
Diffraction is split off using the shower
enhancement factor c (Baker 1976).
pi
diff
1 c tot
(bi , s)
( pi (bi , s) pi (bi , s))
c
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.
2n
2n
f ( x1 , x2 ,..., x2 n 1 , x2 n ) f 0 u ( xi ) (1 xi )
h
i 1
h
pi
i 1
QGS model for , N, 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
Diffractive String model
Hadron and nucleon exchange momentum
Longitudinal momentum exchange excites
hadron and nucleon
These independently hadronize into
secondary hadrons
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 , <Pt2>=0.9 GeV2
Average multiplicities
p H X 200 GeV/c
Average multiplicity
per particle type
enlarged scale
M.Gazdzicki, O.Hansen, Nucl.Phys. A58(1991) 754
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
QGS Model - Invariant cross section
E d 3
[ GeV mb/(GeV/c)3 sr Nucleon ]
3
Ad p
Pions from Proton (400GeV/c) scattering off Ta
70°
90°
118°
Ekin [GeV]
137°
160°
Solid dots:
N.A.Nikiforov et.al.
Phys.Rev.C22(1980) 754
Ekin [GeV]
Ekin [GeV]
Diffractive Model - Invariant cross section
E d 3
[ GeV mb/(GeV/c)3 sr Nucleon ]
3
Ad p
Pions from Proton (400GeV/c) scattering off Ta
70°
90°
118°
Ekin [GeV]
137°
160°
Solid dots:
N.A.Nikiforov et.al.
Phys.Rev.C22(1980) 754
Ekin [GeV]
Ekin [GeV]
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