微視的輸送模型
微視的輸送模型:JAM:JAM
奈良 寧 (Nara, Yasushi)
国際教養大学 (Akita International Univ.)
高エネルギー重イオン衝突におけるハドロンカスケード模型
モデルの説明: インプット (ハドロン散乱レベルでの素過程)
Resonance production,string, hard scattering
応用例
まとめセミナー J-PARC Tokai , Aug. 7 2013

開発動機
Microscopic transport models for nuclear collisions at intermediate energies

1988 BUU (PR160, Bertsch,Gupta)
1990 BUU (PR188, Giessen)
1991 QMD (PR202, Aichelin)
1993 RBUU (RPP56,Giessen)JAPAN (Kyoto Horiuch group)
1990 VUU (A.Ohnishi)
1990 QMD (T. Maruyama)
1992 AMD (A.Ono)
1995 QMD (Niita)

Monte-Carlo event generator for high energy hadronic collisions
PYTHIA (Lund model)
HERWIG
VENUS

FRITIOF
QGSM
RQMD, UrQMD

1996-2000 JAMを開発 (主に原研のポスドク時代)

HIJING

High energy heavy ion collision
Pb+Pb collision at E=200 AGeV
Animation
fromHdronic
Cascademodel
JAMAfter the collision,matter looks like this.
UrQMD simulation

Hot and dense matter created!

Gold beam-beam collision event at
RHIC experimentHadronic transport models
OSCAR (Open Standard Codes and Routines)
http://karman.physics.purdue.edu/OSCAR/index.php/Main_Page

RQMD
UrQMD

Frankfurt group: http://th.physik.uni-frankfurt.de/~urqmd/

GiBUU

The Giessen Boltzmann-Uehling-Uhlenbeck project
http://gibuu.physik.uni-giessen.de/GiBUU/

JAM

http://quark.phy.bnl.gov/~ynara/jam/
http://www.aiu.ac.jp/~ynara/jam

Y.Nara, N.Otuka, A.Ohnishi, K.Niita and S.Chiba, Phys. Rev. C61, 024901 (2000)
T. Hirano and Y. Nara PTEP 2012 (2012)01A203

Applications of hadronic cascade model
hadron-nucleus collisions (proton, pion, kaon,....)
Nucleus-nucleus collisions
Gamma-nucleus collisions

Hydrodynamics + hadron cascadeParton cascade + hadron cascade
GIANT4Air shower model of cosmic ray

Hadron cascade の簡単な説明
Initial state (before collision): Nucleons are sampled according toWoods-Saxon distribution, momentum of each nucleon is sampled
by Fermi momentum,
boost two nucleus according to the corresponding incident energy.

ハドロン-ハドロン散乱の インコヒーレントな重ね合わせ

2. Straight line trajectories until particles interact
3. Collision at closest approach d    tot /Geometrical interpretation of cross section

Incident hadronpion

Outgoing channel selection:
prob. of elastic =  el totすてべの可能な素過程
粒子発生の時空発展

Closest distance approach
Closest distance between two colliding particles is defined bybX'Collision time

The two collision times are in general different in the lab. Frame.

Physics of elementary processes
AGS 10GeV以下
Resonance excitations: e.g.

SPS 200GeV

String excitations

RHIC/LHC energies and above
pQCD Hard process and CGC

Hadronic Cross sections in JAM

Resonance production (absorption)

String formation

Parametrization of the Resonanceproductions in pp

Modeling low energy π-p cross sections
S-channel inelastic:
pi-p -> resonance (or string)
T-channel inelastic:
pi-p -> resonance + resonance
Elastic
Charge exchange:

 − p  0 n

Kaon + proton inelastic

Anti-kaon + proton inelastic

Other elementary processes
Resonance absorption process: detailed balance formula

Cross section from the Additive quark modelJAM: total cross sections

String
Stringexcitation
excitationand
anddecay
decayabove
aboveresonanceresonanceregion
regionZ

String excitation of hadrons

String decay into hadrons

Leading hadrons

incident hadrons

after string excitation in FRITIOF,HIJING, and JAM models.
quark content is the same.

after string excitation in DPM,
VENUS models, quark fromdifferent hadron is connected
due to color exchange.

String excitation

DPM (dual parton model) type momentum transfer:

The Lund Model
B. Andersson, G. Gustafson, G. Ingelman and T. Sjostrand,``Parton Fragmentation And String Dynamics,''

Phys. Rept. 97, 31 (1983).

PYTHIA6.4 Physics and Manual 489pages
JHEP 0605:026 (2006)

String breaking
E A=  x A − x 0  , E B =  x 0 − x B p A = t A −t 0  , p B = t 0 −t B 2m22=
x−x

−t−t
ABAB2m2O

 xO , t O B  x B , t BA  x A , t A

質量は実数であるから、Vertex AとBの間は空間的であり、なんの因果関係もない。
特別なvertexはない.
qbarqString decay by the Lund string model
破砕過程がquarkとantiquakのどちらから行っても同じである (left-right symmetry)と要請すれば、破砕関数の形は一意に決まる。
Lund symmetric fragmentation functionū
u : d d̄ : s ̄s : c ̄c =1: 1: 0.3 :10−11
≈0.5,∗K
≈0.6∗
K K

Different from statistics∗D≈0.75∗
D D

Hadron formation pointfrom string decay

Spacetime pictureof q-qbar string motion

Eikonal Formulation for pQCD(HIJING)

T. Sjostrand and M. van Zijl, Phys. Rev. D36 (1987)2019

Pythia hadronic collisions
Hard scattering (pQCD) + soft interaction (longitudinal excitation)+ hadronization via string fragmentation.
= K ∫ dx 1 dx 2 dt f 1  x1, Q 2  QCD f 2  x 2, Q 2 String-drawing issues
Color flow についてはMatrix element の干渉項は無視 (1/N_c^2)g g  g g Process in proton-proton collisiongg

Proton-proton collisions at 12 GeV/c

Pion production cross sections in JAM

Excitation function of p+p -> xin JAM

Proton distribution
at AGS energy

pion distribution
at AGS energy(E=14GeV)Transverse momentum distribution
at SPS energy (160AGeV)Rapidity distributions

Nucl-th/0102051

High energy heavy ion collisions

τ=0CGCτ≈1/Q sτ≈1∼2 fm/c

Non equilibrium

Hydro evolution Hadron gastimeCollective behavior
Elliptic flow
Y
Target Spectator Projectile Spectator

Coordinatespace〈 y 2 −x 2 〉= 2 2〈x y 〉Momentumspacev 2=〈 〉2222px − pypx  py

InitialXParticipantsv 2 ≡〈 cos  2  〉=〈2222px − p ypx  p y〉

AfterIdea : Interaction ➩ convert space anisotropy to momentum anisotropy

Hadronic dissipative effect on theelliptic flowtime

Phys.Rev. C77 (2008) 044909

hadron gas

QGP fluid
collision axis
0AuAu

(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka et al., Hirano et al.

Possible improvements in JAM
More systematic implementation of elementary processes● Low energy particle productions● Direct pion/kaon production● Latest PDF● CGC?
● C++ version● いろいろupdateしたいがFortranのままだと無理● 現在はバグフィックスのみ。
● Explicit treatment of spacetime evolution of partons●

-+(K ,K ) reactions
This is not JAM results.
 N  K  , K  ∗ 1530
K N  , a0, f 0  K
 , a0 , f 0  K  K − N  ,  , ,  ,  'Y , Y ∗K ,  ,  ,  , ' N 
 K , K ∗ Y , Y ∗  , N
Y.Nara, A.Ohnishi, T.Harada and A.Engel, Nucl. Phys. A614, 433 (1997)

まとめ

ハドロニックカスケードモデルは、重イオン衝突や、ハドロン-原子核反応の古典的時空発展をミクロに記述するものである。
現時点ですべての 素過程 を満足できる形で導入したモデルはない。
現在最高エネルギーで原子核を衝突できるRHIC energy まで、粒子の multiplicity などのバルクな観測量はよく再現できるが、集団効果,例えば楕円形フローなどは再現できない。