Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
1
Steffen A. Bass
Duke University
•
RHIC: the emerging picture
•
Modeling of Relativistic Heavy

Ion Collisions
•
Relativistic Fluid Dynamics
•
Hybrid Macro+Micro Transport
•
Model Validation: RHIC
•
Predictions for LHC
•
Spectra & Yields
•
Collective Flow
•
Transport Coefficients: Low Viscosity Matter at LHC?
Dynamics of hot & dense QCD matter:
from RHIC to LHC
collaborators:
•
J. Ruppert
•
T. Renk
•
C. Nonaka
•
B. Mueller
•
A. Majumder
•
M. Asakawa
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
2
RHIC:
the emerging picture
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
3
Exploring QCD Matter at RHIC and LHC
initial state
pre

equilibrium
QGP and
hydrodynamic expansion
hadronization
hadronic phase
and freeze

out
Lattice

Gauge
Theory:
•
rigorous calculation of QCD quantities
•
works in the infinite size / equilibrium limit
Experiments:
•
observe the final state + penetrating probes
•
rely on QGP signatures predicted by Theory
Phenomenology &
Transport Theory:
•
connect QGP state to observables
•
provide link between LGT and data
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
4
Current Picture of QGP Structure:

Lessons from RHIC

Jet

Qenching & Elliptic Flow:
•
QGP produced at RHIC has very large opacity
•
behaves like an ideal fluid (vanishing viscosity)
Lattice Gauge Theory & Parton Recombination:
•
at T
C
, QGP degrees of freedom carry the quantum numbers of
quarks and recombine to form hadrons
Applicability of Ideal Fluid Dynamics and Statistical Model:
•
matter produced is thermalized
•
thermalization (isotropization) occurs very early, ~0.6 fm/c
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
5
Modeling of
Relativistic Heavy

Ion Collisions
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
6
Survey of Transport Approaches
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
7
Relativistic Fluid Dynamics
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
8
Relativistic Fluid Dynamics
•
transport of macroscopic degrees of freedom
•
based on conservation laws:
μ
T
μν
=0
μ
j
μ
=0
•
for ideal fluid:
T
μν
= (
ε
+p) u
μ
u
ν

p g
μν
and j
i
μ
=
ρ
i
u
μ
•
Equation of State
needed to close system of PDE’s:
p=p(T,
ρ
i
)
connection to Lattice QCD calculation of EoS
•
initial conditions (i.e. thermalized QGP) required for calculation
•
assumes local thermal equilibrium, vanishing mean free path
applicability of hydro is a strong signature for a thermalized system
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
9
3D

Hydro: Validation at RHIC
separate chemical f.o.
simulated by rescaling p,K
•
1
st
attempt to address
all data w/ 1 calculation
b=6.3 fm
Nonaka & Bass:
PRC75, 014902 (2007)
See also Hirano; Kodama et al.
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
10
Ideal RFD: Challenges
•
centrality systematics of v
2
less than perfect
•
no flavor dependence of cross

sections
•
separation chemical and kinetic freeze

out:
•
normalize spectra by hand
•
PCE: proper normalization, wrong v
2
Nu Xu
Viscosity:
•
success of ideal RFD argues for a low
viscosity in QGP phase
compatible with AdS/CFT bound of 1/4
π
•
viscosity will stongly change as function
of temperature during collision
need to account for viscous corrections
in hadronic phase
Csernai
HG: Prakash et al.
QGP: Arnold,
Moore & Yaffe
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
11
Hybrid Hydro+Micro Approaches
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
12
Full 3

d Hydrodynamics
QGP evolution
Cooper

Frye
formula
UrQMD
t fm/c
hadronic
rescattering
Monte Carlo
Hadronization
T
C
T
SW
Bass & Dumitru, PRC61,064909(2000)
Teaney et al, nucl

th/0110037
Nonaka & Bass, PRC75, 014902 (2007)
Hirano et al. nucl

th/0511046
3D

Hydro + UrQMD Model
•
ideally suited for dense systems
–
model early QGP reaction stage
•
well defined Equation of State
•
parameters:
–
initial conditions
–
Equation of State
Hydrodynamics
+
micro. transport (UrQMD)
•
no equilibrium assumptions
model break

up stage
calculate freeze

out
includes viscosity in hadronic phase
•
parameters:
–
(total/partial) cross sections
matching condition:
•
use same set of hadronic states for EoS as in UrQMD
•
generate hadrons in each cell using local T and
μ
B
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
13
3D

Hydro+UrQMD: Validation
good description of
cross section dependent
features & non

equilibrium features of
hadronic phase
hydrodynamic evolution
used for calculation of
hard probes
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
14
Predictions for LHC
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
15
Initial Conditions @ LHC
required for all hydro

based calculations
•
can be obtained from:
ab

inito calculations of initial state
analysis of LHC data
phenomenological extrapolation of RHIC data
PHOBOS extrapolation:
•
extend longitudinal scaling
•
self

similar trapezoidal shape
Saturation model scaling:
•
ASW: dN
ch
/d
=1650
•
KLN:
dN
ch
/d
=1800

2100
•
EHNRR: dN
ch
/d
=2570
U. Wiedemann
QM06
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
16
3D

Hydro+UrQMD: Initial Conditions
•
Initial Conditions:
–
energy density
–
baryon number density
–
parameters:
–
flow profile:
•
Equation of State
–
1st order phase transition
–
T
c
=160 MeV
•
switching temperature
–
T
SW
=150 MeV
v
T
=0
v
L
=
Bjorken’s solution);
0
,
max
, n
Bmax
,
0
,
RHIC
LHC

Bj
LHC

1
LHC

2
0
(fm)
0.6
0.3
0.2
0.2
0
(GeV/fm
3
)
55
230
1000
500
0
0.5
N/A
1.0
1.0
1.4
N/A
6.0
6.0
transverse plane
•
note that LHC

Bj initial conditions were not meant to provide a
reasonable guess for LHC but rather elucidate a scenario more
extreme than RHIC
longitudinal profile
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
17
Spectra & Yields
Disclaimer:
•
do not take the following “predictions” too seriously
•
they only represent placeholders to demonstrate the capabilities of this
particular transport approach
•
once data are available, the parameters of the initial condition will be
adjusted in order to establish whether 3D

Hydro+UrQMD can provide a
viable description of QGP dynamics at LHC
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
18
Blast from the Past: Bj

Hydro+UrQMD
SAB & A. Dumitru: Phys. Rev. C61 064909 (2000):
•
boost

invariant 1+1D RFD with UrQMD as hadronic afterburner
•
RFD validated with SPS data
[Dumitru & Rischke: PRC59 354 (1999)]
dynamic transition from QGP &
mixed phase to hadronic phase
•
increase in <p
t
> as function of hadron
mass less than linear due to flavor

dependence of hadronic rescattering
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
19
From SPS to LHC
•
from RHIC to LHC: lifetime of QGP phase nearly doubles
•
only 33% increase in collision numbers of hadronic phase
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
20
3D

Hydro+UrQMD: Multiplicities
dN/dy
at y
CM
LHC

1
LHC

2
+
1715
904
K
+
228
123
p
57
34
0
+
0
33
19
+
4.3
2.5

0.85
0.52
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
21
3D

Hydro+UrQMD: Spectra
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
22
3D

Hydro+UrQMD: dissipative effects
•
significant dissipative effects
early chemical freeze

out manifest
in proton distribution (pure Hydro
would need PCE)
•
hadronic phase “cools” pion
spectrum
•
built

up of radial flow for
heavier particles
pion wind
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
23
Hybrid RFD+Boltzmann Summary
•
validated at RHIC for soft sector and jet energy

loss
•
treatment of viscosity in hadronic phase
•
separation of thermal & chemical freeze

out
allows for consistent treatment of bulk matter dynamics and hard probes
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
24
Collective Flow
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
25
Collision Geometry: Elliptic Flow
elliptic flow (v
2
):
•
gradients of almond

shape surface will lead to
preferential emission in the reaction plane
•
asymmetry out

vs. in

plane emission is quantified
by 2
nd
Fourier coefficient of angular distribution: v
2
calculable with fluid

dynamics
Reaction
plane
x
z
y
The applicability of fluid

dynamics
suggests that the medium is in
local thermal equilibrium!
Note that fluid

dynamics cannot
make any statements how the
medium reached the equilibrium
stage…
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
26
spatial
eccentricity
momentum
anisotropy
initial energy density distribution:
Elliptic flow: early creation
time evolution of the energy density:
P. Kolb, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909
Most hydro calculations suggest that flow anisotropies are generated at the
earliest stages of the expansion, on a
timescale of ~ 5 fm/c
if a QGP
EoS is assumed.
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
27
3D

Hydro (+UrQMD): Elliptic Flow
•
dissipative effects in hadronic
phase do not affect built

up of
elliptic flow
robust early time signal
•
no significant sensitivity to the
two initial conditions
( note Kolb, Sollfrank & Heinz:
PLB459 (1999) 667: only small rise)
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
28
Transport Coefficients:
Low Viscosity Matter
M. Asakawa, S.A. Bass & B. Mueller:
Phys. Rev. Lett.
96
(2006) 252301
Prog. Theo. Phys.
116
(2006) 725
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
29
initial state
pre

equilibrium
QGP and
hydrodynamic expansion
hadronization
hadronic phase
and freeze

out
Viscosity: from RHIC to LHC
expanding hadron gas
w/ significant & increasing
mean free path:
large viscosity
large elliptic flow
& success of ideal RFD:
zero/small viscosity
•
viscosity of matter changes strongly with time & phase
•
Hydro+UrQMD: viscous corrections for hadron gas phase
•
how to understand low viscosity in QGP phase?
•
will low viscosity features persist at LHC?
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
30
The sQGP Dilemma
•
microscopic transport theory shows
that assuming quasi

particle q & g
degrees of freedom would require
unphysically large parton cross
sections to match elliptic flow data
•
even for
λ
0.1 fm (close to uncertainty
bound) dissipative effects are large
does a small viscosity have to imply that matter is strongly interacting?
consider effects of (turbulent) color fields
the success of ideal hydrodynamics has led the community to equate
low viscosity with a vanishing mean free path and thus large parton
cross sections:
strongly interacting QGP (sQGP)
D. Molnar
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
31
Anomalous Viscosity
•
Plasma physics:
–
A.V. = large viscosity induced in nearly collisionless plasmas by long

range fields
generated by plasma instabilities.
•
Astrophysics

dynamics of accretion disks:
–
A.V. = large viscosity induced in weakly magnetized, ionized stellar accretion disks
by orbital instabilities.
•
Biophysics:
–
A.V. = The viscous behavior of nonhomogenous fluids, e.g., blood, in which the
apparent viscosity increases as flow or shear rate decreases toward zero.
•
Can the QGP viscosity be anomalous?
–
Expanding plasmas (e.g. QGP @ RHIC) have anisotropic momentum distributions
–
plasma turbulence arises naturally in plasmas with an
anisotropic
momentum
distribution (Weibel

type instabilities).
soft color fields generate
anomalous
transport coefficients
, which may give the
medium the character of a nearly
perfect fluid
even at moderately weak coupling.
Anomalous Viscosity:
any contribution to the shear viscosity not explicitly resulting
from momentum transport via a transport cross section
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
32
Weibel (two

stream) instability
Ultra

Relativistic Heavy

Ion Collision: two streams of colliding color charges
•
consider the effect of a seed magnetic field with
0,0
B p k p
•
induced current creates B, adds to seed B
•
opposing currents repel each other: filamentation
exponential Weibel instability
Guy Moore, McGill Univ.
•
pos. charges deflect
as shown: alternately
focus and defocus
•
neg. charges defocus
where pos. focus and
vice versa
net

current induced,
grows with time
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
33
Hard Thermal Loops: Instabilities
2 2
eq
( ) 1 ( )
f p f p p n
find HTL modes for anisotropic distribution:
for any
ξ
0 there exist unstable modes
energy

density
and growth rate of
unstable modes can be calculated:
Romatschke & Strickland, PRD
68
: 036004 (2003)
Arnold, Lenaghan & Moore, JHEP
0308
, 002 (2003)
Mrowczynski, PLB
314
, 118 (1993)
a
a c
ab
a
c
b
dp dQ
gQ u gf
F
u Q
d d
A
Nonabelian Vlasov equations describe interaction of
“hard”
(i.e. particle) and
“soft”
color field modes and generate the “hard

thermal loop” effective theory:
2
HTL
2
2
1
4
( )
( )
2
ab
a a a b
g C
p p
dp
f p
p
L
F F F F
p D
Effective HTL theory permits systematic study of instabilities of “soft” color fields:
( ) ( ) ( ) ( ( ))
i i i
i
J x d Q u x x
g
D F
J
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
34
Anomalous Viscosity Derivation: Sketch
•
linear Response: connect
η
with momentum anisotropy
Δ
:
•
use color Vlasov

Boltzmann Eqn. to solve for
f
and
Δ
:
•
Turbulent color field assumption:
•
ensemble average over fields:
diffusive Vlasov

Boltzmann Eqn:
•
example: anomalous viscosity in case of transverse magnetic fields
•
complete calculation of
η
via variational principle:
3 4
0
3
2
1
15
2
p p
f
d p
T E E
p
p
,
0
,,,
a
p
a
f t f
v g C
t f
x
r p r p
F
(mag) (mag)
,
a b a a
i j i j
ab
U
x x
x x t t
x x
B B B B
,,0
,,
p p
v f t C
D f
f
x
t
p
p
r
r
(gluo
6
a
n)
2
2 m g
16 6 1
c
c
m
A
N
T
N
g
2
B
2
(quark)
6
2
2 mag
62 6
f
m
A
c
N N
T
g
2
B
1 1 1
A C
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
35
collisional viscosity:
•
derived in HTL weak coupling limit
anomalous viscosity:
•
induced by turbulent color fields, due to momentum

space anisotropy
•
with ansatz for fields:
for reasonable values of g:
A
<
C
Collisional vs. Anomalous Viscosity
4 1
5
ln
C
s g g
3/5
0
2
A
T
c
s g u
M. Asakawa, S.A. Bass & B. Mueller:
Phys. Rev. Lett.
96
(2006) 252301
Prog. Theo. Phys.
116
(2006) 725
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
36
Time

Evolution of Viscosity
initial state
pre

equilibrium
QGP and
hydrodynamic expansion
hadronization
hadronic phase
and freeze

out
A C
A C
A C
HG
1
1
1
A
C
A
C
HG
viscosity:
? ?
•
relaxation rates are additive
sumrule for viscosities:
smaller viscosity dominates
in system w/ 2 viscosities!
temperature
evolution:
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
37
Viscosity at LHC: Two Scenarios
field picture:
•
(turbulent) color fields induce an anomalous viscosity, which keeps
the total shear

viscosity small during the QGP evolution
perfect liquidity in the weak coupling limit
collisional picture:
•
weaker coupling at LHC vs. RHIC will lead to a larger viscosity
increase in dissipative effects, deviations from ideal fluid
elliptic flow at LHC compared to RHIC can act as a decisive
measurement for the dominance of anomalous viscosity
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
38
Summary and Outlook
•
Heavy

Ion collisions at RHIC have produced a state of matter which
behaves similar to an ideal fluid
Hydro+Micro transport approaches are the best tool to describe the
soft, non

perturbative physics at RHIC after QGP formation
at LHC, such hybrid models should perform well if QGP matter is
found to have a low viscosity
•
a small viscosity does not necessarily imply strongly interacting
matter!
(turbulent) color fields induce an anomalous viscosity, which keeps
the total sheer

viscosity small during the QGP evolution
elliptic flow at LHC as decisive measurement on impact of anomalous
viscosity
Note:
•
due to it’s slow & nearly isotropic expansion,
the early Universe most likely did not have an
anomalous contribution to its viscosity
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
39
The End
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #
40
Elliptic Flow: ultra

cold Fermi

Gas
•
Li

atoms released from an optical trap exhibit
elliptic flow analogous to what is observed in ultra

relativistic heavy

ion collisions
Elliptic flow is a general feature of strongly
interacting systems!
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