Transcript QGP and Dynamics of Relativistic Heavy Ion Collisions Tetsufumi Hirano

QGP and Dynamics of
Relativistic Heavy Ion
Collisions
Tetsufumi Hirano
The University of Tokyo, Komaba
Thermal Quantum Field Theories and Their Applications
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
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
History of the Universe
~ History of Matter
Quark Gluon
Plasma
Hadronization
Nucleosynthesis
QGP study
Understanding
early universe
Little Bang!
Relativistic Heavy Ion Collider(2000-)
RHIC as a time machine!
STAR
front
view
STAR
Collision energy
100 GeV per nucleon
Au(197×100)+Au(197×100)
Multiple production
(N~5000)
Heat
side
view
BASIC CHECKS
Basic Checks (I): Energy Density
Bjorken energy density
observables
t: proper time
y: rapidity
R: effective transverse radius
mT: transverse mass
Bjorken(’83)
Critical Energy Density from Lattice
Stolen from Karsch(PANIC05);
Note that recent results seem to be Tc~190MeV
Centrality Dependence of Energy
Density
ec from lattice
PHENIX(’05)
Well above
ec from lattice
in central
collision at RHIC,
if assuming
t=1fm/c.
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?
Gyulassy, Matsui(’84) Ruuskanen(’84)
• Averaged over transverse area. Effect of
thickness? How to estimate area?
Basic Checks (II): Chemical Eq.
direct
Resonance decay
Two fitting parameters: Tch, mB
Amazing fit!
T=177MeV, mB = 29 MeV
Close to Tc from lattice
CAVEATS (II)
• Even e+e- or pp data can be fitted well!
See, e.g., Becattini&Heinz(’97)
• What is the meaning of fitting
parameters?
• Why so close to Tc?
See, e.g., Rischke(’02),Koch(’03)
 No chemical eq. in hadron phase!?
 Essentially dynamical problem!
Expansion rate  Scattering rate
(Process dependent)
see, e.g., U.Heinz, nucl-th/0407067
Basic Checks (III): Radial Flow
Driving force of flow
pressure gradient
Inside: high pressure
Outside: vacuum (p=0)
Blast wave model (thermal+boost)
Spectrum for heavier particles
is a good place to see radial flow.
Sollfrank et al.(’93)
Spectrum change is seen in AA!
O.Barannikova, talk at QM05
Power law in pp & dAu
Convex to Power law
in Au+Au
•“Consistent” with
thermal + boost
picture
•Large pressure
could be built up in
AA collisions
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?
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
Dynamics of Heavy
Ion Collisions:
Elliptic Flow and Perfect Liquid
Dynamics of Heavy Ion Collisions
Freezeout
“Re-confinement”
Expansion, cooling
Thermalization
First contact
(two bunches of gluons)
Time scale
10fm/c~10-23sec
Temperature scale
100MeV~1012K
Why Hydrodynamics?
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
Static
•EoS from Lattice QCD
•Finite T, m field theory
•Critical phenomena
•Chiral property of hadron
What is Elliptic Flow?
Ollitrault (’92)
How does the system respond to spatial anisotropy?
No secondary interaction
Hydro behavior
y
f
x
INPUT
Spatial Anisotropy
2v2
OUTPUT
dN/df
dN/df
Interaction among
produced particles
Momentum Anisotropy
0
f
2p
0
f
2p
Time Evolution of a QGP Fluid
TH&Gyulassy(’06)
QGP
mixed
hadron
Anisotropy of energy density distribution
 Anisotropy of “Momentum” distribution
Time Evolution of v2 from a Parton
Cascade Model
Zhang et al.(’99)
ideal hydro limit
v2
: Ideal hydro
b = 7.5fm
: strongly
interacting
system
t(fm/c)
generated through secondary collisions
v2 is saturated in the early stage
sensitive to cross section (~1/m.f.p.~1/viscosity)
Schematic Picture of Shear
Viscosity
See, e.g. Danielewicz&Gyulassy(’85)
Assuming relativistic particles,
Shear flow
Smearing of flow
Perfect fluid:
l=1/sr  0
shear viscosity  0
Next time step
Basis of the Announcement
response =
(output)/(input)
STAR(’02)
PHENIX(’03)
“Hydro limit”
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.
Recent Hydro
Results
from Our Group
TH et al. (’06).
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(’02); TH and K.Tsuda(’02);
TH et al. (’06).
Pseudorapidity Dependence of v2
QGP+hadron
QGP only
h<0 h=0
h>0
•v2 data are comparable
with hydro results again
around h=0
•Not a QGP gas  sQGP
•Nevertheless, large
discrepancy in
forward/backward rapidity
See next slides
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
Hadron Gas Instead of Hadron Fluid
A QGP fluid surrounded
by hadronic gas
QGP core
QGP: Liquid (hydro picture)
Hadron: Gas (particle picture)
See also talk/poster by Nonaka
“Reynolds number”
Matter proper part:
(shear viscosity)
(entropy density)
big
in Hadron
small
in QGP
Importance of Hadronic “Corona”
QGP fluid+hadron gas
QGP+hadron fluids
QGP only
•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!?
T.Hirano et al.,Phys.Lett.B636(2006)299.
QGP Liquid + Hadron Gas Picture
Works Well
20-30%
Mass dependence is o.k.
Note: First result was obtained
by Teaney et al.
•Centrality dependence is ok
•Large reduction from pure
hydro in small multiplicity
events
T.Hirano et al.,Phys.Lett.B636(2006)299.
Some Comments
on the Discovery
1. Is mass ordering for v2(pT) a
signal of the perfect QGP fluid?
Pion
20-30%
Proton
Mass dependence is o.k. from
hydro+cascade.
Mass ordering comes from
rescattering effect. Interplay
btw. radial and elliptic flows
Not a direct sign of the
perfect QGP fluid
2. Is viscosity really small in QGP?
•1+1D 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!
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?!
Digression
[Pa] = [N/m2]
(Dynamical) Viscosity h:
~1.0x10-3 [Pa s] (Water 20℃)
~1.8x10-5 [Pa s] (Air 20℃)
Kinetic Viscosity n=h/r:
~1.0x10-6 [m2/s] (Water 20℃)
~1.5x10-5 [m2/s] (Air 20℃)
hwater > hair BUT nwater < nair
Non-relativistic Navier-Stokes eq. (a simple form)
Neglecting external force and assuming incompressibility.
3. Is h/s enough?
•Reynolds number
Iso, Mori, Namiki (’59)
R>>1
Perfect fluid
•(1+1)D Bjorken solution
•Need to solve viscous fluid dynamics in (3+1)D
 Cool! But, tough!
 Causality problem (talk by Kunihiro, talk/poster by Muroya)
4. Boltzmann at work?
Molnar&Gyulassy(’00)
Molnar&Huovinen(’04)
gluonic
fluid
25-30%
reduction
s ~ 15 * spert !
Caveat 1: Where is the “dilute” approximation in Boltzmann
simulation? Is l~0.1fm o.k. for the Boltzmann description?
Caveat 2: Differential v2 is tricky. dv2/dpT~v2/<pT>.
Difference of v2 is amplified by the difference of <pT>.
Caveat 3: Hadronization/Freezeout are different.
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 1+1D).
Being smaller T0 from pT dist., t0 should be larger (~10fm/c).
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!
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
Hadron Gas instead of Hadron Fluid
Hadronic
Corona
(Cascade,
JAM)
t
z
0
sQGP core
(Full 3D
Hydro)
(Option)
Color Glass
Condensate
Glauber-BGK and CGC Initial Conditions
Which Clear the First Hurdle
Centrality dependence
Rapidity dependence
Glauber-BGK
•Glauber model
Npart:Ncoll = 85%:15%
•CGC model
Matching I.C. via e(x,y,h)
CGC
pT Spectra for identified hadrons
from QGP Hydro+Hadronic Cascade
dN/dy and dN/dpT are o.k. by hydro+cascade.
Caveat: Other components such as recombination and
fragmentation should appear in the intermediate-high pT regions.
Results from Hydro + Cascade
Glauber-BGK
CGC
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
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?????????????????
20-30%
History of differential elliptic flow
~History of development of hydro
~History of removing ambiguity in hydro
Temperature Dependence of h/s
•Shear Viscosity in Hadron Gas
Danielewicz&Gyulassy(’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:
Viscosity from a Kinetic Theory
See, e.g. Danielewicz&Gyulassy(’85)
For ultra-relativistic particles, the shear viscosity is
Ideal hydro:
l0
Transport cross section
shear viscosity  0
Schematic Picture of Shear
Viscosity
See, e.g. Danielewicz&Gyulassy(’85)
Assuming relativistic particles,
Shear flow
Smearing of flow
Perfect fluid:
l=1/sr  0
shear viscosity  0
Next time step
A Long Long Time Ago…
…we obtain the value R (Reynolds number)=1~10…
Thus we may infer that the assumption of the
perfect fluid is not so good as supposed by Landau.
h/s from Lattice
I love to
see this
region!!
A.Nakamura and S.Sakai,PRL94,072305(2005).
Shear viscosity to
entropy ratio from
lattice (pure gauge)
+ an assumption
of spectral function
eta/s < 1
is one of the
promising results of
applicability for
hydro at RHIC
Challenging calculation!
Navier-Stokes Eq. and Relaxation
Time
cf.)杉山勝、数理科学(2002年８月号）
•Non-rela. (Cattaneo (’48))
Balance Eq.
Constitutive Eq.
t0: Fourier law
t : relaxation time
Violation of
causality
Heat Eq. (Hyperbolic Eq.)
Finite relaxation time
Telegraph Eq.(Parabolic Eq.)
Mueller,Israel,Stewart,…
Novel Viscous Fluid Dynamics
Balance Eqs
How to get constitutive eqs.?
2nd thermodynamic law
Constitutive
Eq.
1st order
2nd order
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(1±n) Israel,Stewart
Can it be obtained from Lattice?
How Do Partons Get Longitudinal
Momentum in Comoving System?
Free Streaming eta=y
Sheet:
eta=const
dN/dy
dN/dy
Sum of delta function
y
Width “Thermal” fluctuation
y
22 Collisions Do Not Help!
Only 22 collisions,
partons are still in a
transverse sheet
eta~y~const.
23 may help.
Xu and Greiner, hep-ph/0406278
h/s from MD simulations
eta/s has a minimum
in the vicinity of Tc !
Y.Akimura et al., nucl-th/0511019
No thermal qqbar
production
Preliminary result
Statistical Model Fitting to ee&pp
Becattini&Heinz(’97)
Phase space dominance?
“T” prop to E/N? See, e.g., Rischke(’02),Koch(’03)
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.
A Closer Look Reveals Details of
Hadronic Matter
Stolen from M.Bleicher (The Berkeley School)
How Reliable Quantitatively?
f, W?
Small
rescattering
System
expands
like this
trajectory?
Radial flow in pp collisions?