Steffen A. Bass

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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!