The Quest for the
Quark-Gluon-Plasma
Steffen A. Bass
• Introduction: QCD and the Quark-Gluon-Plasma
• Experimental and Theoretical Techniques
• Recent Discoveries: the case for the QGP
•
•
•
•
jet energy-loss
the (almost) perfect liquid
turbulence and anomalous viscosity
parton recombination
work supported through grants by:
Steffen A. Bass
M. Asakawa
R.J. Fries
A. Majumder
B. Mueller
C. Nonaka
T. Renk
J. Ruppert
The Quest for the QGP #1
11 Science Questions for the New Century
• formulated by the National Research Council:
1.
2.
3.
What is dark matter?
What is dark energy?
How were the heavy elements from Iron
to Uranium made?
4. Do neutrinos have a mass?
5. Where do ultra-high energy particles
come from?
6. Is a new theory of light and matter
needed to explain what happens at very
high energies and temperatures?
7. Are there new states of matter at ultrahigh temperatures and densities?
8. Are protons unstable?
9. What is gravity?
10. Are there additional dimensions?
11. How did the Universe begin?
Steffen A. Bass
The Quest for the QGP #2
Introduction
• Quantum Chromodynamics (QCD)
• Quark-Gluon-Plasma
Steffen A. Bass
The Quest for the QGP #3
QCD: The Basics
u
• Quantum-Chromo-Dynamics (QCD)
•
•
•
•
one of the four basic forces of nature
basic constituents of matter: quarks and gluons
is responsible for most of the mass of ordinary matter
holds protons and neutrons together in atomic nuclei
d
u
•Confinement & Asymptotic Freedom:
•
•
•
•
quarks and gluons carry color charge (RGB)
only color-neutral bound states are observed
coupling diverges as large distances / small Q2
at small distances / large Q2 q’s and g’s roam freely
effective coupling
(αs = ｇ２/４π）
• The QCD vacuum: ground-state of QCD
• has a complicated structure
• contains scalar and vector condensates
uu  dd  0 and G  G  0
• explore vacuum-structure by heating/melting QCD matter
 Quark-Gluon-Plasma
Steffen A. Bass
The Quest for the QGP #4
2004 Nobel Prize in Physics
Steffen A. Bass
The Quest for the QGP #5
Phases of Normal Matter
solid
liquid
gas
 electromagnetic interactions
determine phase structure of
normal matter
Steffen A. Bass
The Quest for the QGP #6
Phases of QCD Matter
• strong interaction analogues of the
familiar phases:
• Nuclei behave like a liquid
– Nucleons are like molecules
• Quark Gluon Plasma:
– “ionize” nucleons with heat
– “compress” them with pressure
 new state of matter!
Steffen A. Bass
The Quest for the QGP #7
QCD on the Lattice
Goal: explore the thermodynamics of QCD
 evaluate QCD partition function:
   n e  H n 
n

n e  H n1 n1 e  H n2
nN e  H n
n , n1 , , nN
 path integral with N steps in imaginary time
 can be numerically calculated on a 4D Lattice
Equation of State for an ideal QGP:
  30 gDOFT
2
4
(ultra-relativistic gas of massless bosons)
F. Karsch
Steffen A. Bass
 LGT predicts a phase-transition
to a state of deconfined nearly
massless quarks and gluons
 QCD becomes simple at high
temperature and/or density
The Quest for the QGP #8
QGP and the Early Universe
• few microseconds
after the Big Bang the
entire Universe was in
a QGP state
• compressing &
heating nuclear matter
allows to investigate
the history of the
Universe
• the only means of
recreating temperatures
and densities of the early
Universe is by colliding
beams of ultra-relativistic
heavy-ions
Steffen A. Bass
The Quest for the QGP #9
Telescope for the Early Universe:
The Relativistic Heavy-Ion Collider
Steffen A. Bass
The Quest for the QGP #10
Brookhaven National Laboratory
Steffen A. Bass
The Quest for the QGP #11
Detectors at RHIC
• solenoid as centerpiece
• total detector weight: 1200 tons
• TPC: tracking of 1000s of particles
simultaneously
• can record dozens Au+Au collisions
per second
Example: STAR Detector
• 52 institutions, 12 countries
• 529 collaborators
• construction cost: 80 M$
Steffen A. Bass
The Quest for the QGP #12
Collisions at RHIC
• typical collision recorded by the STAR detector: Au+Au @ 200 GeV/NN-pair
• 1000s of tracks have to be reconstructed to determine species and momenta
of produced hadrons and characterize collision
Steffen A. Bass
The Quest for the QGP #13
Lifting the veil of confinement:
Transport Theory
• Microscopic Models for ultra-relativistic heavy-ion collisions
- S.A. Bass et al, Prog. Part. Nucl. Phys. 41 (1998) 225
• Dynamics of hot bulk QCD matter: from the QGP to hadronic freeze-out
- S.A. Bass and A. Dumitru, Phys. Rev. C61 (2000) 064909
• Parton Rescattering and Screening in Au+Au at RHIC
- S. A. Bass, B. Mueller and D.K. Srivastava, Phys. Lett. B551 (2003) 277
Steffen A. Bass
The Quest for the QGP #14
Time-Evolution of a Heavy-Ion Collision
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
Transport-Models • full description of collision dynamics
& Phenomenology: • connects intermediate state to observables
• provides link between LGT and data
Steffen A. Bass
The Quest for the QGP #15
Microscopic Transport Models
microscopic transport models describe the time-evolution
of a system of (microscopic) particles by solving a transport
equation derived from kinetic theory
key features:
• describe the dynamics of a many-body system
• connect to thermodynamic quantities
• take multiple (re-)interactions among the dof’s into account
key challenges:
• quantum-mechanics: no exact solution for the many-body problem
• covariance: no exact solution for interacting system of relativistic particles
• QCD: limited range of applicability for perturbation theory
Steffen A. Bass
The Quest for the QGP #16
Kinetic Theory:
- formal language of transport models classical approach:
Liouville’s Equation:
f N
 f N , H  0
t
use BBKGY hierarchy and cut off at 1-body level
a) interaction based only on potentials: Vlasov Equation
 p
 1



(

U
)

r
p f  0
 t m r

b) interaction based only on scattering: Boltzmann Equation
with
 p  1
 t  m  r  f  I coll
I coll  N   d  dp2 v1  v2  f1 ( p1) f1 ( p2 )  f1 ( p1 ) f1 ( p2 ) 
Steffen A. Bass
The Quest for the QGP #17
Collision Integral: Monte-Carlo Treatment
• f1 is discretized into a sample of microscopic particles
• particles move classical trajectories in phase-space
• an interaction takes place if at the time of closes approach dmin of
two hadrons the following condition is fulfilled:
d min 
 tot

with  tot   tot
 s, h
1
, h2

• main parameter:
– cross section: probability for an interaction to take place,
which is interpreted geometrically
dmin
Steffen A. Bass
The Quest for the QGP #18
Applying Transport Theory to
Heavy-Ion Collisions
Pb + Pb @ 160 GeV/nucleon (CERN/SPS)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
•calculation done with the UrQMD
(Ultra-relativistic Quantum
Molecular Dynamics) model
•initial nucleon-nucleon collisions
excite color-flux-tubes (chromoelectric fields) which decay into
new particles
•all particles many rescatter
among each other
•initial state: 416 nucleons (p,n)
•reaction time: 30 fm/c
•final state: > 1000 hadrons
Steffen A. Bass
The Quest for the QGP #19
Recent Discoveries:
• the case for the QGP
Steffen A. Bass
The Quest for the QGP #20
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
early times:
• jet production and quenching
• [photons & leptons]
S.A. Bass, D.K. Srivastava & B. Mueller, Phys. Rev. Lett. 90 (2003) 082301
T. Renk, S.A. Bass & D.K. Srivastava, Phys. Lett. B632 (2006) 632
T. Renk, J. Ruppert, C. Nonaka & S.A. Bass, nucl-th/0611027
Steffen A. Bass
The Quest for the QGP #21
Jet-Quenching: Basic Idea
What is a jet?
leading
particle
leading
particle
suppressed
hadrons
hadrons
q
q
q
q
hadrons
hadrons
leading
particle
• fragmentation of hard
scattered partons into
collimated “jets” of hadrons
 p+p reactions provide a
calibrated probe, well
described by pQCD
what happens if partons
traverse a high energy
density colored medium?
Steffen A. Bass
leading
particle
suppressed
• partons lose energy and/or fragment
differently than in the vacuum: radiative
energy loss
q
L
g
q
2
d


qφ   q 2 dq 2 2   kT2 
f
dq
 transport coefficient q is sensitive to
density of (colored) charges
The Quest for the QGP #22
q-hat at RHIC
• suppression can be experimentally
quantified in terms of RAA ratio:
2
RAA
RHIC data
sQGP?
AA
d N dydpT
 2 pp
AA
d N dydpT  N coll
QGP
“Baier plot”
Pion gas
Cold nuclear matter
 RHIC data shows values for q-hat
far larger than expected even for
a QGP!
Steffen A. Bass
The Quest for the QGP #23
Jet-Medium Interactions
•
•

how does a fast moving color charge influence the medium?
can Mach-shockwaves be created?
particle emission patterns should reflect angle of mach-cone
cos  M   cs with cs2  p / 
 data show strong hints of mach-cone formation
 angle indicates surprisingly low speed of sound
•
•
Steffen A. Bass
J. Casalderrey-Solana, E.V. Shuryak & D. Teaney: Nucl. Phys. A774 (2006) 577
T. Renk & J. Ruppert: Phys. Rev. C73 (2006) 011901
The Quest for the QGP #24
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
intermediate times:
• creation of an ideal liquid
• (anomalous) viscosity
S.A. Bass & A. Dumitru, Phys. Rev C61 (2000) 064909
D. Teaney et al, nucl-th/0110037
T. Hirano et al. Phys. Lett. B636 (2006) 299
C. Nonaka & S.A. Bass, Phys. Rev. C (2006) in print
Steffen A. Bass
1999: first hybrid with 1+1D hydro
• won LBNL/INT RHIC predictions prize
• 100+ citations
2006: first full 3D hydro implementation
The Quest for the QGP #25
RHIC in the press: Perfect Liquid
• on April 18th, 2005, BNL
announced in a press release
that RHIC had created a new
state of hot and dense matter
which behaves like a nearly
perfect liquid.
• how does one
measure/calculate the
properties of an ideal liquid?
• are there any other ideal liquid
systems found in nature?
Steffen A. Bass
The Quest for the QGP #26
Relativistic Fluid Dynamics (RFD)
• 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 viscosity
 applicability of hydro is a strong signature for a thermalized system
Steffen A. Bass
The Quest for the QGP #27
Collision Geometry: Elliptic Flow
• two nuclei collide rarely head-on, but mostly with an offset:
Reaction
plane
z
only matter in the overlap area gets
compressed and heated up
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
 RFD: good agreement with data; QGP EoS necessary
Steffen A. Bass
The Quest for the QGP #28
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 model 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
The Quest for the QGP #29
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!
K. M. O’Hara, S. L. Hemmer, M. E. Gehm, S. R. Granade, J. E. Thomas:
Science 298 (2002) 2179
Steffen A. Bass
The Quest for the QGP #30
Viscosity 101
shear and bulk viscosity are defined as the coefficients in the
expansion of the stress tensor in terms of the velocity fields:
 


Tik   uiuk  P  ik  uiuk    iuk   k ui  23  ik   u    ik   u
assuming matter to be quasi-particulate in nature:
microscopic kinetic theory:
 is given by the rate of
momentum transport
  np f 
1
3
p
3 tr
unitarity limit on cross sections
suggest a lower bound for 
4
 tr  2
p
p3
 
12
 viscosity decreases with increasing cross section (forget molasses!!)
 for RFD, the microscopic origin of the viscosity is not important
Steffen A. Bass
The Quest for the QGP #31
Viscosity at RHIC
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 @ RHIC changes strongly with time & phase
• ideal RFD breaks down in later reaction stages
 need to take viscous corrections for hadron gas into account
Steffen A. Bass
The Quest for the QGP #32
3D-Hydro + UrQMD Model
Full 3-d Hydrodynamics
QGP evolution
Hadronization
Cooper-Frye
formula
UrQMD
hadronic
rescattering
Monte Carlo
Hydrodynamics
•
•
•
ideally suited for dense systems
– model early QGP reaction stage
well defined Equation of State
parameters:
– initial conditions
– Equation of State
TC
TSW
t fm/c
+ 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 μB
Steffen A. Bass
The Quest for the QGP #33
3D-Hydro+UrQMD: Results
good agreement with
wide variety of data
• H+U to date the most
successful description
for bulk matter @ RHIC
 confirms very low
viscosity of matter in
the QGP phase
•
Steffen A. Bass
The Quest for the QGP #34
Where does the small viscosity come from?
M. Asakawa, S.A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301
M. Asakawa, S.A. Bass & B. Mueller: Prog. Theo. Phys. 116 (2006) 725
Steffen A. Bass
The Quest for the QGP #35
AdS/CFT correspondence
• calculating viscosity and viscosity/entropy ratio too difficult in full QCD
• quantities are calculable in a related theory using string theory methods
model for QCD:
N = 4 Super-Yang-Mills theory
finite temperature
large NC and strong coupling limit
a string theory in 5d AdS
black hole in AdS5
classical gravity limit
 YM observables at infinite NC and infinite coupling
can be computed using classical gravity
 technique can be applied to dynamical and thermodynamic observables
 in all theories with gravity duals one finds:

s

4
(very small number!)
caution:
• N=4 SUSY YM is not QCD
• no information on how low /s is microscopically generated
Steffen A. Bass
J. Maldacena: Adv. Theor. Math. Phys. 2 (1998) 231
Quest505
for the QGP #36
E. Witten: Adv. Theor. Math. Phys. The
2 (1998)
S.S. Gubser, I.R. Klebanov & M. Polyakov: Nucl.Phys. B636 (2002) 99
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
• gluon densities needed for jetquenching calculations may be too
D. Molnar
large compared to measured entropy
 does a small viscosity have to imply that matter is strongly interacting?
 Paradigm shift needed: consider effects of (turbulent) color fields
Steffen A. Bass
The Quest for the QGP #37
Anomalous Viscosity
Anomalous Viscosity:
 any contribution to the shear viscosity not explicitly resulting from
momentum transport via a transport cross section
•
Plasma physics:
–
•
Astrophysics - dynamics of accretion disks:
–
•
A.V. = large viscosity induced in weakly magnetized, ionized stellar accretion disks by orbital
instabilities.
Biophysics:
–
•
A.V. = large viscosity induced in nearly collisionless plasmas by long-range fields generated by
plasma instabilities.
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, turbulent 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
The Quest for the QGP #38
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
The Quest for the QGP #39
Hard Loops: Instabilities
Nonabelian Vlasov equations describe interaction of “hard” (i.e. particle) and “soft”
color field modes and generate the “hard loop” effective theory:
dp 
 gQ a F a u
d
dQ a
 gf abc Ab u Q c
d
D F   gJ 
J  ( x)    d Qi ( )ui ( )  ( x  xi ( ))
i
• for any anisotropic momentum distribution there exist unstable modes
 energy-density and growth rate of unstable modes can be calculated:
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Romatschke & Strickland, PRD 68: 036004 (2003)
Arnold, Lenaghan & Moore, JHEP 0308, 002 (2003)
Mrowczynski, PLB 314, 118 (1993)
Steffen A. Bass
The Quest for the QGP #40
Anomalous vs. Collisional 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
 T
 c0  2
s
 g u
A



3/ 5
• Note that for reasonably small values in the coupling:
A
s
Steffen A. Bass

C
s
The Quest for the QGP #41
Collisional vs. Anomalous Viscosity
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
initial state
pre-equilibrium
temperature
evolution:
•
 A  C
cross sections are additive
• ηλf1/σ
 sumrule for viscosities:
hadronization
 A  C
1


1
A
 A  C

1
C
 HG
 smaller viscosity dominates
in system w/ 2 viscosities!
 anomalous viscosity dominates total shear viscosity during QGP evolution
 a small viscosity does not necessarily imply strongly interacting matter!
Steffen A. Bass
The Quest for the QGP #42
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
Dynamics of Hadronization
• The baryon puzzle at RHIC
• Recombination + Fragmentation Model
• quark-number scaling of elliptic flow
R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 (2003) 202303
R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 (2003) 044902
C. Nonaka, R.J. Fries & S.A. Bass, Phys. Lett. B 583 (2004) 73
R. J. Fries, S.A. Bass & B. Mueller, PRL 94 (2005) 122301
Steffen A. Bass
featured in Thompson ESI:
Fast Moving Fronts March 2005
2004 JNS publication prize for
Young Nuclear Theorists awarded
to C. Nonaka
500+ citations since January 2003
The Quest for the QGP #43
The baryon puzzle @ RHIC
species dependence of v2 saturation:
• not predicted by RFD
• why do baryons overtake mesons?
• why do protons not exhibit the
v2
same jet- suppression as pions?
 fragmentation starts with a single
fast parton: energy loss affects
pions and protons in the same way!
Steffen A. Bass
The Quest for the QGP #44
Recombination+Fragmentation Model
basic assumptions:
• at low pt, the quarks and antiquark spectrum is
thermal and they recombine into hadrons
locally “at an instant”:
V
d 3q
 CM
w
3
3 
3
d P
(2 ) (2 )
dN M

1
2

Pq w
1
2

P  q φM (q)
2
• at high pt, the parton spectrum is given by a
pQCD power law, partons suffer jet energy loss
and hadrons are formed via fragmentation
of
1
quarks and gluons: E dN h  d P  u dz  w (R, 1 P)D
d 3P

(2 )3 0 z 2


z
 h
(z)
• Reco: baryons shifted to higher pt than mesons, for same quark distribution
• shape of spectrum determines if reco or fragmentation is more effective:
• for thermal distribution recombination yield dominates fragmentation yield
• vice versa for pQCD power law distribution
 understand behavior of baryons, since jet-quenching is strictly high-pt!
Steffen A. Bass
The Quest for the QGP #45
Reco: Single Particle Observables
 consistent description of spectra, ratios and RAA
Steffen A. Bass
The Quest for the QGP #46
Parton Number Scaling of v2
•in leading order of v2,
recombination predicts:
p 
2v2p  t 
 2
v2M  pt  
2
M
 p  pt  p

1  2  v2   
2
t   2 2
 pt 
v  p   2v  
2
and
 p    p 
3v    3  v   
3  
Bv  p    3  p   p
v2  pt  1 36 vv2 p   t 
3  3
 

3
p
2
B
2
p
2
t
t
t
2
p
2
t
 smoking gun for recombination
 measurement of partonic v2 !
Steffen A. Bass
Most direct deconfinement
signature to date!
The Quest for the QGP #47
Dynamic Modeling: Discovery to Exploration
• Dynamical Modeling provides insight into the microscopic reaction
dynamics of a heavy-ion collision and connects the data to the properties
of the deconfined phase and rigorous Lattice-Gauge calculations
• a variety of different conceptual approaches exist, developed to address
the physics relevant to specific stages of the collision
• a “standard model” covering the entire time-evolution of a heavy-ion
reaction remains to be developed
 develop suite of validated and
mutually interfaced transport
codes for modeling all stages
of the collision
 perform simultaneous
parameter optimization for the
quantitative extraction of key
QGP and transport parameters
from data
 multi-institutional project with
Duke in strong leadership role
Steffen A. Bass
The Quest for the QGP #48
Summary and Conclusion
• Heavy-Ion collisions at RHIC have produced a
deconfined state of matter which can be called a
QGP research utilizes
Quark-Gluon-Plasma
insights from:
 the QGP has the properties of a near ideal fluid
• QCD
with a (very) small viscosity
• Lattice field theory
 (turbulent) color fields induce an anomalous
• kinetic/transport theory
viscosity, which keeps the total shear-viscosity
small during the QGP evolution
• statistical mechanics
 parton recombination shows direct evidence for
• fluid dynamics
the built-up of collectivity in the deconfined
• plasma physics
phase
• string theory
Note:
• AMO: Fermi-systems
• due to its slow & nearly isotropic expansion,
the early Universe most likely did not have an
anomalous contribution to its viscosity
Steffen A. Bass
The Quest for the QGP #49
The End
Steffen A. Bass
The Quest for the QGP #50
The Practical Side of Heavy-Ion Collisions
Suppose…
•
You lived in a frozen world where water existed only as ice
•
and ice comes in only quantized sizes ~ ice cubes
•
and theoretical friends tell you there should be a liquid phase
•
and your only way to heat the ice is by colliding two ice cubes
•
So you form a “bunch” containing a billion ice cubes
•
which you collide with another such bunch
•
10 million times per second
•
which produces about 1000 IceCube-IceCube collisions per second
•
which you observe from the vicinity of Mars
 Change the length scale by a factor of ~1013
 You’re doing physics at RHIC!
Steffen A. Bass
The Quest for the QGP #51
The RHIC Facility
• 2.4 miles round, 12 ft underground
• 1740 superconducting magnets
• 1,600 miles of superconducting
niobium titanium wire
• helium chiller draws 15 MW of power
(enough for 15,000 homes)
RHIC tunnel
• gold beams travel at 99.995% c
(186,000 miles per second)
• beam made up of 57 bunches
• collisions at 4 intersection points
• temperature in collisions is 150,000
times temperature of the sun
Steffen A. Bass
RF Cavity system
The Quest for the QGP #52
Initial Particle Production in UrQMD
Steffen A. Bass
The Quest for the QGP #53
AdS/CFT correspondence
• calculating viscosity and viscosity/entropy ratio too difficult in full QCD
• quantities are calculable in a related theory using string theory methods
model for QCD: N = 4 Super-YangMills theory in 4d with SU(NC)
a string theory in 5d AdS
finite temperature
black hole in AdS5
large NC and strong coupling limit
classical gravity limit
 YM observables at infinite NC and infinite coupling
can be computed using classical gravity
 technique can be applied to dynamical and thermodynamic observables
J. Maldacena: Adv. Theor. Math. Phys. 2 (1998) 231
E. Witten: Adv. Theor. Math. Phys. 2 (1998) 505
S.S. Gubser, I.R. Klebanov & M. Polyakov: Nucl.Phys. B636 (2002) 99
Steffen A. Bass
The Quest for the QGP #54
/s bound in QCD from AdS/CFT
• viscosity from Kubo’s formula:
1
i t
Txy t, x ,Txy 0, 0 
  lim
dt
dx
e
 0 2 
R
 lim lim Gxy,
xy ( ,q)
 0 q0
AdS/CFT correspondence:
Imaginary part of retarded Greensfunction
is mapped on graviton absorption cross section
 abs  
16 G

G R ( )
 abs (0)

16 G
• viscosity  graviton absorption cross section:
• absorption cross section = area of horizon A
• entropy S=A/4G
 in all theories with gravity duals one finds:

s

4
(very small number!)
caution:
• N=4 SUSY YM is not QCD
• no information on how low /s is microscopically generated
Steffen A. Bass
The Quest for the QGP #55
The RHIC Transport Initiative
Duke Univ. – Ohio State – Michigan State – Purdue – U. of Minnesota
Steffen A. Bass
The Quest for the QGP #56
Hard Loops: Instabilities
Nonabelian Vlasov equations describe interaction of “hard” (i.e. particle) and “soft”
color field modes and generate the “hard loop” effective theory:
dp 
 gQ a F a u
d
dQ a
 gf abc Ab u Q c
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:
g 2C2 dp
p p
a
a
a
b
1
LHTL  F F 
f
(
p
)
F
F

4
2  p
( p  D) 2
ab
find HTL modes for anisotropic distribution:
f ( p )  1   f eq

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
The Quest for the QGP #57
Anomalous Viscosity Derivation: Sketch
• linear Response: connect η with momentum anisotropy Δ:
1
 
15T
f 0
d 3 p p4
  2 3 E p2   p  E p
• use color Vlasov-Boltzmann Eqn. to solve for f and Δ:

a
a
v
f
r
,
p
,
t

g
F

f


 r , p, t   C  f   0
p

x

• Turbulent color field assumption:
• ensemble average over fields: Bia  x U ab  x, x  B jb  x   Bia B ja (mag)  t  t   (mag)  x  x 
 diffusive Vlasov-Boltzmann Eqn: v 

f  r, p, t    p  D  p f  r, p, t   C  f   0

x
• example: anomalous viscosity in case of transverse magnetic fields
2
2
6
6
62

6
N
N


T
16

6
N

1



T
c
f
(quark
)
c
A

 A(gluon ) 
2
2
mag
2
g 2 B 2  mmag
 Nc
g B m
Steffen A. Bass
The Quest for the QGP #58