QGP and Dynamics of Relativistic Heavy Ion Collisions

1
QGP and Dynamics of Relativistic Heavy Ion
Collisions

• Tetsufumi Hirano
• The University of Tokyo, Komaba

Thermal Quantum Field Theories and Their
Applications
2
OUTLINE
My Charge To interpret recent experimental data
at RHIC from a QGP fluid dynamics point of view

• Basic Checks
• Energy density
• Chemical and kinetic equilibrium
• Dynamics of Heavy Ion Collisions
• Elliptic Flow and Perfect Liquid!?
• Recent Results from Hydro models
• Some Comments on the Discovery
• Summary and Outlook

3
Physics of the QGP

• Matter governed by QCD, not QED
• High energy density/temperature frontier
• ?Toward an ultimate matter (Maximum energy
  density/temperature)
• Understanding the origin of matter which evolves
  with our universe
• Reproduction of QGP in H.I.C.
• ?Reproduction of early universe on the Earth

4
History of the Universe History of Matter
Quark Gluon Plasma Hadronization Nucleosynthesis
QGP study Understanding early universe
5
Little Bang!
front view
Relativistic Heavy Ion Collider(2000-) RHIC as a
time machine!
STAR
side view
STAR
Collision energy Multiple production (N5000) He
at
100 GeV per nucleon Au(197100)Au(197100)
6
BASIC CHECKS
7
Basic Checks (I) Energy Density
Bjorken energy density
observables
t proper time y rapidity R effective
transverse radius mT transverse mass
Bjorken(83)
8
Critical Energy Density from Lattice
Stolen from Karsch(PANIC05) Note that recent
results seem to be Tc190MeV
9
Centrality Dependence of Energy Density
Well above ec from lattice in central collision
at RHIC, if assuming t1fm/c.
ec from lattice
PHENIX(05)
10
CAVEATS (I)

• Just a necessary condition in the sense that
  temperature (or pressure) is not measured.
• How to estimate tau?
• If the system is thermalized, the actual energy
  density is larger due to pdV work.
• Boost invariant?
• Averaged over transverse area. Effect of
  thickness? How to estimate area?

Gyulassy, Matsui(84) Ruuskanen(84)
11
Basic Checks (II) Chemical Eq.
direct
Resonance decay
Two fitting parameters Tch, mB
12
Amazing fit!
T177MeV, mB 29 MeV
Close to Tc from lattice
13
CAVEATS (II)

• Even ee- or pp data can be fitted well!
• See, e.g., BecattiniHeinz(97)
• What is the meaning of fitting parameters?
  See, e.g., Rischke(02),Koch(03)
• Why so close to Tc?
• No chemical eq. in hadron phase!?
• Essentially dynamical problem!

Expansion rate ?? Scattering rate
(Process dependent)
see, e.g., U.Heinz, nucl-th/0407067
14
Basic Checks (III) Radial Flow
Blast wave model (thermalboost)
Driving force of flow ?pressure gradient Inside
high pressure Outside vacuum (p0)
Sollfrank et al.(93)
Spectrum for heavier particles is a good place to
see radial flow.
15
Spectrum change is seen in AA!
Power law in pp dAu
Convex to Power law in AuAu

• Consistent with thermal boost picture
• Large pressure could be built up in AA collisions

O.Barannikova, talk at QM05
16
CAVEATS (III)

• Not necessary to be thermalized completely
• Results from hadronic cascade models.
• How is radial flow generated dynamically?
• Finite radial flow even in pp collisions?
• (T,vT)(140MeV,0.2)
• Is blast wave reliable quantitatively?
• Consistency?
• Chi square minimum located a different point for
  f and W
• Flow profile? Freezeout hypersurface? Sudden
  freezeout?

17
Basic Checks ? Necessary Conditions to Study QGP
at RHIC

• Energy density can be well above ec.
• Thermalized?
• Temperature can be extracted.
• Why freezeout happens so close to Tc?
• Pressure can be built up.
• Completely equilibrated?

Importance of Systematic Study based on
Dynamical Framework
18
Dynamics of Heavy Ion CollisionsElliptic Flow
and Perfect Liquid
19
Dynamics of Heavy Ion Collisions
Freezeout Re-confinement Expansion,
cooling Thermalization First contact (two
bunches of gluons)
Temperature scale 100MeV1012K
Time scale 10fm/c10-23sec
20
Why Hydrodynamics?

• Static
• EoS from Lattice QCD
• Finite T, m field theory
• Critical phenomena
• Chiral property of hadron

Once one accepts local thermalization
ansatz, life becomes very easy.
Energy-momentum
Conserved number

• Dynamic Phenomena in HIC
• Expansion, Flow
• Space-time evolution of
• thermodynamic variables

21
What is Elliptic Flow?
Ollitrault (92)
How does the system respond to spatial anisotropy?
Hydro behavior
No secondary interaction
y
f
x
INPUT
Spatial Anisotropy
2v2
Interaction among produced particles
dN/df
dN/df
OUTPUT
Momentum Anisotropy
f
0
2p
f
0
2p
22
Time Evolution of a QGP Fluid
THGyulassy(06)
QGP
mixed
hadron
Anisotropy of energy density distribution ?
Anisotropy of Momentum distribution
23
Time Evolution of v2 from a Parton Cascade Model
Zhang et al.(99)
ideal hydro limit
v2
Ideal hydro
strongly interacting system
b 7.5fm
t(fm/c)
generated through secondary collisions
saturated in the early stage sensitive to cross
section (1/m.f.p.1/viscosity)
v2 is
24
Schematic Picture of Shear Viscosity
See, e.g. DanielewiczGyulassy(85)
Assuming relativistic particles,
Perfect fluid l1/sr ? 0 shear viscosity ? 0
Smearing of flow
Shear flow
Next time step
25
(No Transcript)
26
Basis of the Announcement
PHENIX(03)
STAR(02)
Hydro limit
response (output)/(input)
pT dependence and mass ordering
Multiplicity dependence
Hydro results Huovinen, Kolb, Heinz,
It is found that they reproduce v2(pT) data
accidentally.
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
27
Recent Hydro Resultsfrom Our Group
28
Centrality Dependence of v2
TH et al. (06).

• 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)
29
Pseudorapidity Dependence of v2
TH(02) TH and K.Tsuda(02) TH et al. (06).
QGPhadron

• v2 data are comparable with hydro results again
  around h0
• Not a QGP gas ? sQGP
• Nevertheless, large discrepancy in
  forward/backward rapidity
• ?See next slides

QGP only
h0
hlt0
hgt0
30
Hadron Gas Instead of Hadron Fluid
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
A QGP fluid surrounded by hadronic gas
Reynolds number
QGP core
Matter proper part (shear viscosity) (entropy
density)
big in Hadron
small in QGP
QGP Liquid (hydro picture) Hadron Gas (particle
picture)
See also talk/poster by Nonaka
31
Importance of Hadronic Corona

• Boltzmann Eq. for hadrons instead of
  hydrodynamics
• Including viscosity through finite mean free path

QGP fluidhadron gas
QGPhadron fluids
QGP only

• Suggesting rapid increase of entropy density
• Deconfinement makes hydro work at RHIC!?
• ? Signal of QGP!?

T.Hirano et al.,Phys.Lett.B636(2006)299.
32
QGP Liquid Hadron Gas Picture Works Well
20-30

• Centrality dependence is ok
• Large reduction from pure hydro in small
  multiplicity events

Mass dependence is o.k. Note First result was
obtained by Teaney et al.
T.Hirano et al.,Phys.Lett.B636(2006)299.
33
Some Commentson the Discovery
34
1. Is mass ordering for v2(pT) a signal of the
perfect QGP fluid?
Pion
20-30
Proton
Mass ordering comes from rescattering effect.
Interplay btw. radial and elliptic flows ?Not a
direct sign of the perfect QGP fluid
Mass dependence is o.k. from hydrocascade.
35
2. Is viscosity really small in QGP?

• 11D Bjorken flow Bjorken(83)
• Baym(84)Hosoya,Kajantie(85)Danielewicz,Gyulassy(
  85)Gavin(85)Akase et al.(89)Kouno et al.(90)

(Ideal)
(Viscous)
h shear viscosity (MeV/fm2), s entropy
density (1/fm3)
h/s is a good dimensionless measure (in the
natural unit) to see viscous effects.
Shear viscosity is small in comparison with
entropy density!
36
A Probable Scenario
TH and Gyulassy (06)
h shear viscosity, s entropy density
Kovtun,Son,Starinets(05)

• Absolute value of viscosity

• Its ratio to entropy density

!
Rapid increase of entropy density can make hydro
work at RHIC. Deconfinement Signal?!
37
Digression
Pa N/m2
(Dynamical) Viscosity h 1.0x10-3 Pa s
(Water 20?) 1.8x10-5 Pa s (Air 20?)
Kinetic Viscosity nh/r 1.0x10-6 m2/s
(Water 20?) 1.5x10-5 m2/s (Air 20?)
hwater gt hair BUT nwater lt nair
Non-relativistic Navier-Stokes eq. (a simple form)
Neglecting external force and assuming
incompressibility.
38
3. Is h/s enough?

• Reynolds number

Iso, Mori, Namiki (59)
Rgtgt1 ?Perfect fluid

• (11)D Bjorken solution

• Need to solve viscous fluid dynamics in (31)D
• Cool! But, tough!
• Causality problem (talk by Kunihiro, talk/poster
  by Muroya)

39
4. Boltzmann at work?
MolnarGyulassy(00)
MolnarHuovinen(04)
25-30 reduction
gluonic fluid
s 15 spert !
Caveat 1 Where is the dilute approximation in
Boltzmann simulation? Is l0.1fm o.k. for the
Boltzmann description? Caveat 2 Differential v2
is tricky. dv2/dpTv2/ltpTgt. Difference of v2 is
amplified by the difference of ltpTgt. Caveat 3
Hadronization/Freezeout are different.
40
5. Does v2(pT) really tell us smallness of h/s in
the QGP phase?
D.Teaney(03)

• Not a result from dynamical calculation, but a
  fitting to data.
• No QGP in the model
• t0 is not a initial time, but a freeze-out time.
• Gs/t0 is not equal to h/s, but to 3h/4sT0t0 (in
  11D).
• Being smaller T0 from pT dist., t0 should be
  larger (10fm/c).

41
6. Is there model dependence in hydro
calculations?
Novel initial conditions from Color Glass
Condensate lead to large eccentricity.
Hirano and Nara(04), Hirano et al.(06) Kuhlman
et al.(06), Drescher et al.(06)
For CGC, see also talk/poster by Itakura
Need viscosity even in QGP!
42
Summary and Outlook

• We have discovered something really intriguing
  at RHIC
• Perfect QGP fluid and dissipative hadron gas
• Hydro at work as a signal of deconfinement(?)
• Large cross section among partons is needed.
• Still a lot of work needed
• Initial stage, thermalization time,
• h and h/s are not sufficient to discuss viscous
  aspects in H.I.C. (Perfect fluid is a dynamic
  concept.)
• Beyond Boltzmann/ideal hydro approach?
• Success and challenge of hydrodynamics

43
(No Transcript)
44
Hadron Gas instead of Hadron Fluid
Hadronic Corona (Cascade, JAM)
t
sQGP core (Full 3D Hydro)
z
0
(Option) Color Glass Condensate
45
Glauber-BGK and CGC Initial ConditionsWhich
Clear the First Hurdle
Centrality dependence
Rapidity dependence
Glauber-BGK
CGC

• Glauber model
• NpartNcoll 8515
• CGC model
• Matching I.C. via e(x,y,h)

46
pT Spectra for identified hadronsfrom QGP
HydroHadronic Cascade
dN/dy and dN/dpT are o.k. by hydrocascade.
Caveat Other components such as recombination
and fragmentation should appear in the
intermediate-high pT regions.
47
Results from Hydro Cascade
Glauber-BGK
CGC
48
v2(pT) from Hydro Past, Present and Future
2000 (Heinz, Huovinen, Kolb) Ideal hydro w/
chem.eq.hadrons 2002 (TH,Teaney,Kolb) Chemical
freezeout 2002 (Teaney) Dissipation in hadron
phase 2005 (BNL) RHIC serves the perfect
liquid. 2004-2005 (TH,Gyulassy) Mechanism of
v2(pT) slope 2005-2006(TH,Heinz,Nara,) Color
glass condensate Future To be or not to be
(consistent with hydro), that is THE question
-- anonymous
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
?????????????????
20-30
History of differential elliptic flow History of
development of hydro History of removing
ambiguity in hydro
49
Temperature Dependence of h/s

• Shear Viscosity in Hadron Gas

DanielewiczGyulassy(85)

• Assumption h/s at Tc in the sQGP is 1/4p

Kovtun, Son, Starinets(05)
No big jump in viscosity at Tc!

• We propose a possible scenario

50
Viscosity from a Kinetic Theory
See, e.g. DanielewiczGyulassy(85)
For ultra-relativistic particles, the shear
viscosity is
Ideal hydro l ? 0 shear viscosity ? 0
Transport cross section
51
Schematic Picture of Shear Viscosity
See, e.g. DanielewiczGyulassy(85)
Assuming relativistic particles,
Perfect fluid l1/sr ? 0 shear viscosity ? 0
Smearing of flow
Shear flow
Next time step
52
A Long Long Time Ago
we obtain the value R (Reynolds
number)110 Thus we may infer that the
assumption of the perfect fluid is not so good as
supposed by Landau.
53
h/s from Lattice
Shear viscosity to entropy ratio from lattice
(pure gauge) an assumption of spectral function
I love to see this region!!
eta/s lt 1 is one of the promising results
of applicability for hydro at RHIC
A.Nakamura and S.Sakai,PRL94,072305(2005).
Challenging calculation!
54
Navier-Stokes Eq. and Relaxation Time
cf.)????????(2002?8??)

• Non-rela. (Cattaneo (48))

Balance Eq.
Constitutive Eq.
t?0 Fourier law
t relaxation time
Heat Eq. (Hyperbolic Eq.) Finite
relaxation time Telegraph Eq.(Parabolic Eq.)
Violation of causality
55
Novel Viscous Fluid Dynamics
Mueller,Israel,Stewart,
Balance Eqs
How to get constitutive eqs.?
1st order
2nd order
2nd thermodynamic law
Constitutive Eq.
56
Toward determination of transport coefficient of
the QGP

• Navier-Stokes eq. (1st order)

(Linear Response) (Transport Coefficient)
x (Thermodynamic Force)
Lattice QCD Kubo formula
bulk, shear, heat conductivity
Nakamura,Sakai

• Novel rela. visc. fluid dynamics (2nd order)

Relaxation for viscosity It can be obtain from a
comp. btw. Boltzmann Eq. and visc. fluid
dynamics. ? Higher order moment for n(1n) Can it
be obtained from Lattice?
Israel,Stewart
57
How Do Partons Get Longitudinal Momentum in
Comoving System?
Free Streaming etay
Sheet etaconst
dN/dy
dN/dy
Width ?Thermal fluctuation
Sum of delta function
y
y
58
2?2 Collisions Do Not Help!
Only 2?2 collisions, partons are still in
a transverse sheet etayconst. 2?3 may help.
Xu and Greiner, hep-ph/0406278
59
h/s from MD simulations
eta/s has a minimum in the vicinity of Tc !
No thermal qqbar production ?Preliminary result
Y.Akimura et al., nucl-th/0511019
60
Statistical Model Fitting to eepp
BecattiniHeinz(97)
Phase space dominance? T prop to E/N?
See, e.g., Rischke(02),Koch(03)
61
Hadron phase below Tch in H.I.C.

• chemically frozen ? Themalization can be
  maintained through elastic scattering.
• There still exit quasi-elastic collisions, e.g.
• The numbers of short-lived resonances can be
  varied. (Acquirement of chemical potential)
• Recent data suggests importance of (process
  dependent) hadronic rescattering
• Hard to describe this by hydro.

62
A Closer Look Reveals Details of Hadronic Matter
Stolen from M.Bleicher (The Berkeley School)
63
How Reliable Quantitatively?
f, W? Small rescattering
peripheral
System expands like this trajectory?
central
Radial flow in pp collisions?