Transcript Dynamics of hot & dense QCD matter: from RHIC to LHC

Dynamics of hot & dense QCD matter:
from RHIC to LHC
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?
Steffen A. Bass
collaborators:
• J. Ruppert
• T. Renk
• C. Nonaka
• B. Mueller
• A. Majumder
• M. Asakawa
Bulk QCD Matter: from RHIC to LHC #1
RHIC:
the emerging picture
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #2
Exploring QCD Matter at RHIC and LHC
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
initial state
pre-equilibrium
hadronization
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 #3
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 TC, 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 #4
Modeling of
Relativistic Heavy-Ion Collisions
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #5
Survey of Transport Approaches
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #6
Relativistic Fluid Dynamics
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #7
Relativistic Fluid Dynamics
• transport of macroscopic degrees of freedom
• based on conservation laws: μTμν=0 μjμ=0
• for ideal fluid: Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ
• Equation of State needed to close system of PDE’s: p=p(T,ρi)
 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 #8
3D-Hydro: Validation at RHIC
separate chemical f.o.
simulated by rescaling p,K
• 1st attempt to address
all data w/ 1 calculation
Nonaka & Bass:
PRC75, 014902 (2007)
See also Hirano; Kodama et al.
b=6.3 fm
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #9
Ideal RFD: Challenges
• centrality systematics of v2 less than perfect
• no flavor dependence of cross-sections
• separation chemical and kinetic freeze-out:
• normalize spectra by hand
• PCE: proper normalization, wrong v2
Nu Xu
Viscosity:
Csernai
QGP: Arnold,
Moore & Yaffe
HG: Prakash et al.
Steffen A. Bass
• success of ideal RFD argues for a low
viscosity in QGP phase
 compatible with AdS/CFT bound of 1/4π
• viscosity will stongly change as function
of temperature during collision
 need to account for viscous corrections
in hadronic phase
Bulk QCD Matter: from RHIC to LHC #10
Hybrid Hydro+Micro Approaches
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #11
3D-Hydro + UrQMD Model
Full 3-d Hydrodynamics
QGP evolution
Hadronization
Cooper-Frye
formula
UrQMD
hadronic
rescattering
Monte Carlo
Hydrodynamics
•
•
•
TC
TSW
t fm/c
+ micro. transport (UrQMD)
ideally suited for dense systems
– model early QGP reaction stage
well defined Equation of State
parameters:
– initial conditions
– Equation of State
Bass & Dumitru, PRC61,064909(2000)
Teaney et al, nucl-th/0110037
Nonaka & Bass, PRC75, 014902 (2007)
Hirano et al. nucl-th/0511046
Steffen A. Bass
•
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 μB
Bulk QCD Matter: from RHIC to LHC #12
3D-Hydro+UrQMD: Validation
 good description of
cross section dependent
features & nonequilibrium features of
hadronic phase
 hydrodynamic evolution
used for calculation of
hard probes
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #13
Predictions for LHC
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #14
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: dNch/d=1650
• KLN: dNch/d=1800-2100
• EHNRR: dNch/d=2570
Steffen A. Bass
U. Wiedemann
QM06
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Bulk QCD Matter: from RHIC to LHC #15
3D-Hydro+UrQMD: Initial Conditions
• Initial Conditions:
– energy density
 (x, y,)   maxW (x, y;b)H()
longitudinal profile
transverse plane
– baryon number density
nB (x, y,)  nBmaxW (x, y;b)H()
– parameters:
0, max , nBmax, 0, 
– flow profile:
vL=Bjorken’s solution); vT=0
• Equation of State
– 1st order phase transition
– Tc=160 MeV
• switching temperature
– TSW=150 MeV
RHIC
LHC-Bj
LHC-1
LHC-2
0(fm)
0.6
0.3
0.2
0.2
0 (GeV/fm3)
55
230
1000
500
0
0.5
N/A
1.0
1.0

1.4
N/A
6.0
6.0
•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
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #16
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 #17
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 <pt> as function of hadron
mass less than linear due to flavordependence of hadronic rescattering
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #18
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 #19
3D-Hydro+UrQMD: Multiplicities
dN/dy LHC-1 LHC-2
at yCM
Steffen A. Bass
+
1715
904
K+
228
123
p
57
34
0+0
33
19
+
4.3
2.5
-
0.85
0.52
Bulk QCD Matter: from RHIC to LHC #20
3D-Hydro+UrQMD: Spectra
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #21
3D-Hydro+UrQMD: dissipative effects
• hadronic phase “cools” pion
spectrum
• built-up of radial flow for
heavier particles
 pion wind
• significant dissipative effects
 early chemical freeze-out manifest
in proton distribution (pure Hydro
would need PCE)
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #22
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 #23
Collective Flow
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #24
Collision Geometry: Elliptic Flow
Reaction
plane
z
 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…
y
x
elliptic flow (v2):
• gradients of almond-shape surface will lead to
preferential emission in the reaction plane
• asymmetry out- vs. in-plane emission is quantified
by 2nd Fourier coefficient of angular distribution: v2
 calculable with fluid-dynamics
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #25
Elliptic flow: early creation
P. Kolb, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909
time evolution of the energy density:
initial energy density distribution:
spatial
eccentricity
momentum
anisotropy
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 #26
3D-Hydro (+UrQMD): Elliptic Flow
• no significant sensitivity to the
two initial conditions
( note Kolb, Sollfrank & Heinz:
PLB459 (1999) 667: only small rise)
• dissipative effects in hadronic
phase do not affect built-up of
elliptic flow
 robust early time signal
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #27
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 #28
Viscosity: from RHIC to LHC
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
large elliptic flow
& success of ideal RFD:
zero/small viscosity
expanding hadron gas
w/ significant & increasing
mean free path:
large 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 #29
The sQGP Dilemma
 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)
• 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
D. Molnar
 does a small viscosity have to imply that matter is strongly interacting?
 consider effects of (turbulent) color fields
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #30
Anomalous Viscosity
Anomalous Viscosity:
 any contribution to the shear viscosity not explicitly resulting
from momentum transport via a transport cross section
• 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.
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #31
Weibel (two-stream) instability
Ultra-Relativistic Heavy-Ion Collision: two streams of colliding color charges
• consider the effect of a seed magnetic field with B  p  0, k  p  0
• pos. charges deflect
as shown: alternately
focus and defocus
• neg. charges defocus
where pos. focus and
vice versa
 net-current induced,
grows with time
• induced current creates B, adds to seed B
• opposing currents repel each other: filamentation
 exponential Weibel instability
Guy Moore, McGill Univ.
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #32
Hard Thermal Loops: Instabilities
Nonabelian Vlasov equations describe interaction of “hard” (i.e. particle) and “soft”
color field modes and generate the “hard-thermal loop” effective theory:
dp 
 gQ a F a u
d
dQ a
 gf abc Ab u Qc
d
D F   gJ 
J  ( x)    d Qi ( )ui ( )  ( x  xi ( ))
i
Effective HTL theory permits systematic study of instabilities of “soft” color fields:
LHTL  1 F F
4
a

a

p p
b
f ( p) F
F
p
( p  D)2ab
g 2C2 dp
2

a

find HTL modes for anisotropic distribution:
f ( p)  1   feq

p 2   ( p  n )2

 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)
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #33
Anomalous Viscosity Derivation: Sketch
• linear Response: connect η with momentum anisotropy Δ:
f 0
1
d 3 p p4
 

p
 
15T   2 3 E p2
E p
• use color Vlasov-Boltzmann Eqn. to solve for f and Δ:
v

a
a
f
r
,
p
,
t

g
F

f


 r , p, t   C  f   0
p

x
• Turbulent color field assumption:
• ensemble average over fields: Bi  x U ab  x, x  B j  x   Bi B j   t  t     x  x 
 diffusive Vlasov-Boltzmann Eqn: v   f r, p, t    D  f r, p, t  C f  0

 p


 
p

x
a
b
a
a
(mag)
(mag)
• example: anomalous viscosity in case of transverse magnetic fields
16   6  N c  1
T6

 Nc
g 2 B 2  mmag
2

(gluon)
A

(quark )
A

62   6  N c2 N f
2
• complete calculation of η via variational principle:
Steffen A. Bass
g2
T6
B 2  mmag
   
1
1
A
Bulk QCD Matter: from RHIC to LHC #34
1
C
Collisional vs. Anomalous Viscosity
collisional viscosity:
• derived in HTL weak coupling limit
C
5
 4
1
s
g ln g
anomalous viscosity:
• induced by turbulent color fields, due to momentum-space anisotropy
A
s

 O 1

N c2  1
Nc
T6
g
2
B m
2

A
s
:
1
B2
• with ansatz for fields:
 T
 c0  2
s
 g u
A



3/ 5
 for reasonable values of g: A < C
Steffen A. Bass
M. Asakawa, S.A. Bass & B. Mueller:
Phys. Rev. Lett. 96 (2006) 252301
Prog. Theo. Phys. 116 (2006) 725
Bulk QCD Matter: from RHIC to LHC #35
Time-Evolution of Viscosity
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
initial state
pre-equilibrium
viscosity:
 A
• relaxation rates are additive
 sumrule for viscosities:
temperature
evolution:
Steffen A. Bass
hadronization
A  C
 C
??
1


1

1
 A C
A  C
 HG
 smaller viscosity dominates
in system w/ 2 viscosities!
A  C
HG
Bulk QCD Matter: from RHIC to LHC #36
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 #37
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 #38
The End
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #39
Elliptic Flow: ultra-cold Fermi-Gas
• Li-atoms released from an optical trap exhibit
elliptic flow analogous to what is observed in ultrarelativistic heavy-ion collisions
 Elliptic flow is a general feature of strongly
interacting systems!
Steffen A. Bass
Bulk QCD Matter: from RHIC to LHC #40