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