dynamical modeling of heavy ion collisions tetsufumi hirano department of physics the university of...
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Dynamical Modeling ofHeavy Ion Collisions
Tetsufumi HiranoTetsufumi Hirano
Department of PhysicsDepartment of Physics
The University of TokyoThe University of Tokyo
Seminar @ YITP12/10/2008
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OUTLINE
• Introduction• Basic Checks of observables
– Energy density– Chemical and kinetic equilibrium
• Dynamics of Heavy Ion Collisions– Hydrodynamic modeling– Elliptic flow
• Towards precision physics of QGP– Jet quenching (Transport coefficient) – J/psi suppression
• Summary and Outlook
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Two Faces of QCD
Confinement Asymptotic free
q-qbar potentialRunning coupling of QCD
Physics depends on (energy) scale.
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Recipe for QGP
Compress and/or Heat-up!•Density (chemical potential) scale•Temperature scale
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Quark Gluon Plasma
Hadronization
Nucleosynthesis
History of the Universe ~ History of Matter
QGP study
Understandingearly universe
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Little Bang!
Relativistic Heavy Ion Collider(2000-)
RHIC as a time machine!
100 GeV per nucleonAu(197×100)+Au(197×100)
Collision energy
Multiple production(N~5000)
Heat
sideview
frontview
STAR
STAR
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Dynamics of Heavy Ion Collisions
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Dynamics of Heavy Ion Collisions
Time scale10fm/c~10-23sec<<10-4(early universe)
Temperature scale 100MeV~1012K
Freezeout
“Re-confinement”
Expansion, cooling
Thermalization
First contact (two bunches of gluons)
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# of binary collisions
x
y
Thickness function:
Woods-Saxon nuclear density:Gold nucleus:0=0.17 fm-3
R=1.12A1/3-0.86A-1/3
d=0.54 fm
in = 42mb @200GeV
# of participants
1 -( survival probability )
Ncoll & Npart
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Centrality
PHENIX: Correlation btw. BBC and ZDC signals
Npart and Ncoll as a function of impact parameter
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Elliptic Flow
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What is Elliptic Flow?
How does the system respond to spatial anisotropy?
Ollitrault (’92)Ollitrault (’92)
Hydro behavior
Spatial Anisotropy
Momentum Anisotropy
INPUT
OUTPUT
Interaction amongproduced particles
dN
/d
No secondary interaction
0 2
dN
/d
0 2
2v2
x
y
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v2 from a Boltzmann simulation
b = 7.5fm
generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity)
v2 is
Zhang et al.(’99) ideal hydro limit
t(fm/c)
v2 : Ideal hydro
: strongly interactingsystem
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Why Hydrodynamics?
StaticStatic•EoS from Lattice QCDEoS from Lattice QCD•Finite Finite TT, , field theory field theory•Critical phenomenaCritical phenomena•Chiral property of hadronChiral property of hadron
Dynamic Phenomena in HICDynamic Phenomena in HIC•Expansion, FlowExpansion, Flow•Space-time evolution ofSpace-time evolution of thermodynamic variablesthermodynamic variables
Once one accepts localOnce one accepts localthermalization ansatz,thermalization ansatz,life becomes very easy.life becomes very easy.
Energy-momentum:Energy-momentum:
Conserved number:Conserved number:
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Why Hydrodynamics? (contd.)• We would like to understand the QCD matter
under equilibrium.• Lattice QCD is not able to describe dynamics
of heavy ion collisions.• Analyze heavy ion reaction based on a
model with an assumption of local equilibrium, and see what happens and whether it is consistent with data.
• If consistent, it would be a starting point of the physics of QCD matter.
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Freezeout
“Re-confinement”
Expansion, cooling
Thermalization
First contact (two bunches of gluons)
Dynamics of Heavy Ion Collisions
Inputs in hydrodynamic simulations:•Initial condition•Equation of state•Decoupling prescription
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Recent Hydro Results
from Our Group
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QGP fluid + hadronic cascade
0collision axis
tim
e
Au Au
QGP fluid
Initial condition (=0.6fm):1. Glauber model2. (CGC model)QGP fluid:3D ideal hydrodynamics (Tc = 170 MeV)
Massless free u,d,s+ggas + bag const. Hadron phase:1. Tth=100MeV
2. Hadronic cascade (JAM)(Tsw = 169 MeV)
hadron gas
Hybrid approaches:(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak (3D) Nonaka, Bass, Hirano et al.
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Inputs to Hydro: Multiplicity
1.Glauber model Npart:Ncoll = 85%:15%2. CGC model Matching I.C. via e(x,y,s)
Centrality dependence Rapidity dependence
Kharzeev, Levin, and NardiImplemented in hydro by TH and Nara
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pT Spectra for PID hadrons
A hybrid model works well up to pT~1.5GeV/c.Other components (reco/frag) would appear above.
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Centrality Dependence of v2
Discovery of “Large” v2 at RHIC• v2 data are comparable with hydro results.• Hadronic cascade cannot reproduce data.• Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations.
Result from a hadronic cascade (JAM)(Courtesy of M.Isse)
TH et al. (’06).
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Pseudorapidity Dependence of v2
=0 >0<0
•v2 data are comparable with hydro results again around =0•Not a QGP gas sQGP•Nevertheless, large discrepancy in forward/backward rapiditySee next slides
TH(’02); TH and K.Tsuda(’02); TH et al. (’06).
QGP onlyQGP+hadron
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Hadron Gas Instead of Hadron Fluid
QGP coreQGP core
A QGP fluid surrounded by hadronic gas
QGP: Liquid (hydro picture)Hadron: Gas (particle picture)
“Reynolds number”
Matter proper part: (shear viscosity)(entropy density)
bigin Hadron
smallin QGP
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
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Importance of Hadronic “Corona”
•Boltzmann Eq. for hadrons instead of hydrodynamics•Including viscosity through finite mean free path•Suggesting rapid increase of entropy density•Deconfinement makes hydro work at RHIC!? Signal of QGP!?
QGP only QGP+hadron fluids
QGP fluid+hadron gas
T.Hirano et al.,Phys.Lett.B636(2006)299.
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QGP Liquid + Hadron Gas Picture Works Well
Mass dependence is o.k.Note: First result was obtainedby Teaney et al.
20-30%
•Centrality dependence is ok•Large reduction from pure hydro in small multiplicity events
T.Hirano et al.,Phys.Lett.B636(2006)299; Phys.Rev.C77,044909(2008).
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Centrality Dependence of Differential v2
Pions, AuAu 200 GeV
PHENIXPHENIX
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Hybrid Model at Work at sqrt(sNN)=62.4 GeV
Pions, AuAu 62.4 GeV
PHENIXPHENIX
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Differential v2 in Au+Au and Cu+Cu Collisions
Same Npart, different eccentricity
Au+Au Cu+Cu
Same eccentricity, different Npart
Au+Au Cu+Cu
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Eccentricity Fluctuation
Interaction points of participants varyevent by event. Apparent reaction plane also varies. The effect is significant for smaller system such as Cu+Cu collisions
Adopted from D.Hofman(PHOBOS),talk at QM2006
A sample eventfrom Monte CarloGlauber model
i
0
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Initial Condition with Fluctuation
Rotate each i
to true
Throw a diceto choose b:bmin<b<bmax
averageover events
averageover events
E.g.)bmin= 0.0fmbmax= 3.3fmin Au+Au collisionsat 0-5% centrality
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Effect of Eccentricity Fluctuation on v2 (Glauber)
v2(w.rot) ~ 2 v2(w.o.rot) at Npart~350 in AuAuv2(w.rot) ~ 4 v2(w.o.rot) at Npart~110 in CuCu
Significant effects of fluctuation!
CuCuAuAu
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Effect of Eccentricity Fluctuation on v2 (CGC)
CuCuAuAu
CGC + QGP with (small) viscosity + hadronic gas!?
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Toward precisionphysics of QGP
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Lesson from Observational Cosmology
ObservationCOBE, WMAP,…
Taken fromhttp://lambda.gsfc.nasa.gov/
“Best” cosmological parametersC.L.Bennett et al.,Ap.J.Suppl(’03)
CMB tools:CMBFAST, CAMB,
…
CMB tools:CMBFAST, CAMB,
…
Analysis codes play a major role in precision physics.
Hydrodynamic model in H.I.C.
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Tomography
* 平野哲文、浜垣秀樹、「ジェットで探るクォークグルーオンプラズマ」、日本物理学会誌 2004 年 12 月号
CT (computed tomography) scan
“Tomography”1. Known probes: Spectra reliably calculable via pQCD2. Good detector: RHIC experiments!3. Interaction btw. probes and unknowns: Recent development in this field
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Jet Tomography
g g
g
Tool 1. Jet quenching
High “density” matter
Tool 2. Jet acoplanarity
180 deg. correlation?
Bjorken(’82)Gyulassy,PlümerWang (’90)
Bjorken(’82)Appel (’86)Blaizot & McLerran (’86)
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Difference btw. pp and AA
f
f
D
D
a
b
c
d
f’
f’
a
b
Dc
Dd
A×
A×
pp collisions AA collisions
f: Parton distributionD: Fragmentation function
QGP?
JetNucleon
Nucleon
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pT
RAA 1
binary collision scaling
Au+Au 0-10% central•b=2.8 fm
•Ncoll = 978•Npart = 333
•Npart/Ncoll = 0.341
participant scaling0.341
Nuclear Modification Factor
(null result)
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“Transport Coefficient”
R.Baier, hep-ph/0209038
for pQCD
For static medium,
Baier et al.
Stopping power One of the important quantity to characterize
the QGP
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RAA for 0 and IAA for charged
How do we understand this large K?
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J/psi Suppression
Color Screening
cc
M.Asakawa and T.Hatsuda, PRL. 92, 012001 (2004)A. Jakovac et al. PRD 75, 014506 (2007)G.Aarts et al. arXiv:0705.2198 [hep-lat]. (Full QCD)See also T.Umeda,PRD75,094502(2007)
Quarkonium suppression in QGPColor Debye Screening
T.Matsui & H. Satz PLB178 416 (1986)
Suppression depends on temperature (density) and radius of QQbar system.
TJ/psi : 1.6Tc~2.0Tc T, T’ : ~ 1.1Tc
May serve as the thermometer in the QGP.
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Results from Hydro + J/psi Model• Best fit @ (TJ/, T, fFD) = (2.00Tc, 1.34Tc, 10%)
Bar: uncorrelated sys.Bracket: correlated sys.
• Onset of J/ suppression at Npart ~ 160. ( Highest T at Npart~160 reaches to 2.0Tc.)• Gradual decrease of SJ/
tot above Npart~160 reflects transverse area with T>TJ/ increases.• TJ/can be determined in a narrow region.
8
Contour map
1 2
T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007
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Summary and Outlook
• Elliptic flow– QGP fluid + hadron gas picture works well.– Starting Point of finite temperature QCD in
H.I.C.
• Tomography utilizing hydro model– Statistical analysis of jet quenching parameter
(stopping power of high energy partons)
– J/psi suppression above T~2Tc. (Melting temperature of charmonium)
• Toward establishment of the
“observational QGP physics”.