Phenomenological Analysisof High-Energy Heavy-Ion Collisions
Kobayashi-Maskawa Institutefor the Origin of Particles and the Universe
Department of Physics, Nagoya University
Duke University

Chiho NONAKA
January 6, 2017@KMI2017

Quark-Gluon Plasma
RHIC:2000

STAR高T

Heavy Ion Collisions：
LHC,RHIC

Strongly interacting QGP•Relativistic hydrodynamics•Recombination model•Jet quenching•Color Glass Condensate

LHC:2010

Hydrodynamics: QGP, medium

sQGP

Quark-Gluon Plasma

Heavy Ion collisions start!

QCD phase diagram
LHC: Energy frontier
RHIC: Beam Energy Scan
FAIR, NICA, J-PARC：high density

QCD Critical Point
陽子、中間子など

Hadron Phase
Color Super Conductor
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Neutron starμB

Phenomenology for heavy Ion Collisions

Thermalization,sQGP, recombination
Collectivity
QCD phase structure
photonJets
Heavy quarks c, b

medium（light quarks u,d,s)

Phenomenological Models
Time evolution of medium ＋ Observables
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collisions

Heavy Ion Collisionshydrothermalization

hadronization

freezeout

Phenomenological model: Hydrodynamic model• Strong elliptic flow@RHIC
strongly interacting QGP• Shear viscosity@RHIC & LHC• Event-by-event fluctuations• Higher harmonics• Bulk viscosity
Reactionz
plane

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Viscous Hydrodynamic Model• Relativistic viscous hydrodynamic equation for HIC
T µ = ( + p)uµ upg µ + T µ– First order in gradient: acausality– Second order in gradient: which one is suitable for HIC?
• Israel-Stewart, Ottinger and Grmela, AdS/CFT, Grad’s 14momentum expansion, Renormalization group…

• Numerical scheme: small numerical viscosity– First order accuracy: large dissipation
physical viscosities– Second order accuracy : numerical oscillation-> artificial viscosity, flux limiter– Heavy Ion Collisions: SHASTA, KT, HLLE-> Godunov scheme: Riemann solver
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Akamatsu, Inutsuka, CN, Takamoto,arXiv:1302.1665、J. Comp. Phys. (2014)34

K. Okamoto, Y. Akamatsu and CN,Eur.
Phys. J. C76 (2016)579

Numerical Tests in 1Dü Bjorken’s scaling solutions
ü Landau-Khalatnikov Solution (1D)ü Longitudinal fluctuations
ü Conservation property

after 8000 steps
error: 0.01 %C. NONAKA

K. Okamoto, Y. Akamatsu and CN,
Eur. Phys. J. C76 (2016)579

Numerical Tests in 1Dü Bjorken’s scaling solutionsü Landau-Khalatnikov Solution (1D)ü Longitudinal fluctuations
ü Conservation property

K. Okamoto, Y. Akamatsu and CN,
Eur. Phys. J. C76 (2016)579

t0time evolution
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Numerical Tests in 1Dü Bjorken’s scaling solutions
ü Landau-Khalatnikov Solution (1D)ü Longitudinal fluctuations
ü Conservation property

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K. Okamoto, Y. Akamatsu and CN,
Eur. Phys. J. C76 (2016)579

Numerical Tests in 1Dü Bjorken’s scaling solutions
ü Landau-Khalatnikov Solution (1D)ü Longitudinal fluctuations
ü Conservation property

K. Okamoto, Y. Akamatsu and CN,
Eur. Phys. J. C76 (2016)579

Sum of violation of conservation

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Gubser Flow (3D)K. Okamoto, Y. Akamatsu and CN,Eur.
Phys. J. C76 (2016)579

fm-4

fm-4

Energy density Gubser, PRD82 (2010) 085027
t=2fm

t=4 fm
t=3fm
t=5fm

vx

vx
t=2fm

t=3fm
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Dx=Dy=0.05 fm, Dh=0.1

t=4fm

t=5fm

Finite Viscosity• Israel-Stewart Theory

Akamatsu, Inutsuka, CN, Takamoto,arXiv:1302.1665、J. Comp. Phys. (2014)34

Okamoto and CN,in preparation

1. Dissipative fluid equation

Ideal part:
Riemann solver for QGP: Godunov method
Two shock approximation Mignone, Plewa and Bodo, Astrophys. J. S160, 199 (2005)
2. Relaxation equation+advection

stiff equation

I: second order terms
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Poster by Okamoto

Gubser Flow with Finite h/s
Marrochio et al (MUSIC), PRC91, 014903(2015)at y=0= 1.2 fm
= 2.0 fm

= 3.0 fm

= 2.0 fm

= 1.2 fm
= 3.0 fm

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Poster by Okamoto

Gubser Flow with Finite h/s= 3.0 fm

= 1.2 fm

= 2.0 fm

y=0

= 2.0 fm

= 1.2 fm

y=0
= 3.0 fm

x=y

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Poster by Okamoto

Kelvin-Helmholtz Instability

perturbation

Heavy Ion Collsions

Csernai, Strottman,Anderlik, PRC85(2012)054901

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vortexes

higher harmonics
event-by-event fluctuation• Fluctuation in londitudinal direction? on transverse plane• KHI occurs in Heavy Ion collisions?
• Effect on collective flow?
Poster by Okamoto

Kelvin-Helmholtz Instability with Bjorken’s Flow
Fluctuations in initial conditions
ex color flux tubes

Origin of shear flow andfluctuations around vh=0
at mid rapidity

Does KHI happen in an expansion system?
What is the effect on physical observables?
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Poster by Okamoto

Kelvin-Helmholtz Instability with Bjorken’s Flow
• IdealVorticity vector＞
1<y ＞<= 2.0 fm＞ 5.2
1.2 <＞ y <C. NONAKA

6• KHI grows even with
Bjorken’s flow.
• Clear vorticities are observed
at t=5 fm.

= 5.0 fm

＞ y <
＞ 2.6
0.2 <

Poster by Okamoto

KHI with Bjorken’s Flow

• h/s=0.01

1<＞

Vorticity vectory= 2.0 fm＞
0.2 <y ＞<<＞ 6• Vorticities exist, but they are
weaker than those in ideal.
• In the case of h/s=0.08,
vorticities are not formed.

= 5.0 fm

1.6
0.02 <＞

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Poster by Okamoto

Photon Puzzle• LHC Pb+PbsNN = 2760 GeV

Itakura, Fuji and CN in preparation

large v2
~ v2 from hadrons

A hydrodynamic model with latest hadronic photon rates can reproduce
elliptic flow reasonably, but it fails to explain the yield of photon.
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We miss other photon production mechanisms?

Radiative Recombination• Recombination Modelquark

antiquarkgmesonItakura, Fuji and CN in preparation

q,q-barhadronFries, Mueller, Bass, CN, PRL2003, PRC2003

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Solution to• Baryon anomaly in baryon meson ratio,
nuclear modification factor• Quark number scaling in elliptic flow
✗ Energy and entropy conservation

Radiative Recombination

Itakura, Fuji and CN in preparation• Recombination Modelquark

q,q-barg+g
antiquark

hadronmeson

gquarkantiquark

Fries, Mueller, Bass, CN, PRL2003, PRC2003

meson
Resonance particle

ReCo model
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Resonance decay

Solution to• Baryon anomaly in baryon meson ratio,
nuclear modification factor• Quark number scaling in elliptic flow
✗ Energy and entropy conservation

gPossible Solution to Photon
Puzzlequark

Itakura, Fuji and CN in preparation

Resonance from recombination

a.u.

meson
antiquark
Resonance particle

M* ~ 600 MeV
Meson ~ pion
preliminary

k=1 (parameter)
Large yield of photon
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preliminary••

v2 of photon is as large as that of meson!
v2 of photon from resonance decay islarger that that of resonance.

Summary• Hydrodynamic model with state-of-the-art algorithm
Our algorithm– Less artificial diffusion: crucial for viscosity analyses– Stable for strong shock wave
– Test calculations: 1D and 3D– Kelvin-Helmholtz Instability– Now we are ready for experimental analyses @ RHIC and LHC !
Initial condition (TRENTO by Duke), statistical analyses- Future low collision energy experiments at J-PARC and FAIR

• Photon puzzle: large PT distribution and elliptic flow
- Radiative Recombination <- Extension of recombination model
Energy conservation, Deviation of quark number scaling @LHC
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Comparison• Shock Tube Test : Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010)•Analytical solution
TL=0.4 GeV
v=0

EoS: ideal gas•Numerical schemes
SHASTA, KT, NT
Our scheme

TR=0.2 GeV
v=0100
Nx=100, dx=0.1, dt=0.04
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Shocktube Problem• Ideal caseshockwave
rarefaction

Nx=100, dx=0.1, dt=0.04
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L1 Norm• Numerical dissipation: deviation from analytical solution
TL=0.4 GeV
v=0

TR=0.2 GeV
v=0100For analysis of heavy ion collisions
Ncell=100: dx=0.1 fm

Ncell

L(p(Ncell ), p(anaytic)) =i=1|p(Ncell )p(analytic)|Ncell
l=10 fm

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Large DT difference• TL=0.4 GeV, TR=0.172 GeV– SHASTA becomes unstable.
– Our algorithm is stable.

TL=0.4 GeV
v=0• SHASTA: anti diffusion term, Aad– Aad = 1 : default value
0– Aad =0.99: stable,
more numerical dissipation

EoS: ideal gas

TR=0.172 GeV
v=010
Nx=100, dx=0.1, dt=0.04• Large fluctuation (ex initial conditions)– Our algorithm is stable even with small numerical dissipation.

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L1 norm• SHASTA with small Aad has large numerical dissipation
Aad=0.99
Aad=1

TL=400, TR=172

TL=400, TR=200

Ncell

L(p(Ncell ), p(anaytic)) =i=1

C. NONAKA|p(Ncell )p(analytic)|

Ncell

l=10 fmLongitudinal Fluctuations• Propagation of longitudinal fluctuations around Bjorken’s
flow
l=1/3
eB, wh=0:
Bjorken’s solution

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Consistent with Analytical Solutions

Fluctuation dose not propagate and its amplitude decreases.

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Fluctuation propagates and its amplitude decreases.

Conservation Property• Fluctuating initial conditions

Okamoto, Akamatsu, CN, arXiv:1607.03630

Flow
t=10 fm

Energyt=10 fmt0=1 fmt0=1 fmwith source terms

Sum of violation of conservation

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Conservative form

The code based on the conservative form
keeps conservation property with highaccuracy

Our Approach• Israel-Stewart Theory

Takamoto and Inutsuka, arXiv:1106.1732
Akamatsu, Inutsuka, CN, Takamoto, arXiv:1302.1665(ideal hydro)
1. dissipative fluid dynamics = advection + dissipation
exact solution
Contact discontinuity
Shock wave

Riemann solver: Godunov method

Rarefaction wave

Two shock approximation
Mignone, Plewa and Bodo, Astrophys. J. S160, 199 (2005)

Rarefaction wave
2. relaxation equation = advection + stiff equation
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shock wave

Gubser Flow with Finite h/s= 3.0 fm

= 2.0 fm

= 1.2 fmSame conditions in the calculation
except for EoS.

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MUSIC, Marrochio et al, PRC91, 014903(2015)

Shocktube problem• Viscous case

C. NONAKAqt=4.0 fm dt=0.04, 100 steps
analytic

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EoS Dependence

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Numerical Method

Takamoto and Inutsuka, arXiv:1106.1732

SHASTA,rHLLE, KT

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rHLLE vs SHASTA

Schneider et al. J. Comp.105(1993)92

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Artificial and Physical Viscosities
Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010)

Antidiffusion terms : artificial viscosity

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stability

Convergence Speed

Space and time discretization
Second order accuracy
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Numerical Dissipation•numerical dissipation:• from fit of calculated data
1000
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hnum vs Grid Size
Numerical dissipation:Deviation from linear analyses (Llin)

Ex. Heavy Ion Collisionsl ~ 10 fm
0.1<h/s<1
T=500 MeV
Dx << 0.8 – 2.6 fm
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Fluctuating initial conditionl ~ 1 fmDx << 0.25 – 0.82 fm

Riemann Solver in (t,h)-coordinates• Riemann solution

pL

InitialCondition

Okamoto, Akamatsu, CN, arXiv:1607.03630

Cartesian𝑡contact discontinuity

shock wave

shock wave

pL pR

𝑧Pons, Marti, Muller, (2000)

pR(t,h) coordinate

𝜏C. NONAKA

pLpR

ηRiemann Solver in (t,h)-coordinates
Okamoto, Akamatsu, CN, arXiv:1607.03630• Riemann solution

pL

InitialCondition

InitialCondition
shock wave

Cartesian𝑡contact discontinuity
shock wave

pL pR

𝑧Pons, Marti, Muller, (2000)

pR(t,h) coordinate

𝜏C. NONAKA

pLpR

ηRiemann Solver in (t,h)-coordinates

Okamoto, Akamatsu, CN, arXiv:1607.03630• Riemann solution

Cartesian𝑡

shock wave: L

pL

discontinuity(initial)

shock wave

rarefaction
wave

pL pR

shock wave: Rcontact
discontinuity

contact discontinuity

𝑧Pons, Marti, Muller, (2000)

pR(t,h) coordinates𝜏Riemann solution:
Outside of the ligh-cone: Hydrodynamic states(PL and PR) are constant.

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pL

pR

η

Riemann Solver in (t,h)-coordinates

Okamoto, Akamatsu, CN, arXiv:1607.03630• Riemann solution(t,h) coordinates

Cartesian

pL
pL

pR

pR

𝑧

Riemann solution:
Outside of the ligh-cone:
Hydrodynamic states are constant.

𝑧

pL

pR

We can construct the Riemann solverin (t,h) coordiates using that inCartesian coordinates.
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