The Quest for the QGP

1
The Quest for theQuark-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

M. Asakawa R.J. Fries A. Majumder B. Mueller C.
Nonaka T. Renk J. Ruppert
work supported through grants by
2
11 Science Questions for the New Century

• formulated by the National Research Council

• What is dark matter?
• What is dark energy?
• How were the heavy elements from Iron to Uranium
  made?
• Do neutrinos have a mass?
• Where do ultra-high energy particles come from?
• Is a new theory of light and matter needed to
  explain what happens at very high energies and
  temperatures?
• Are there new states of matter at ultra-high
  temperatures and densities?
• Are protons unstable?
• What is gravity?
• Are there additional dimensions?
• How did the Universe begin?

3

• Introduction
• Quantum Chromodynamics (QCD)
• Quark-Gluon-Plasma

4
QCD The Basics

• 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
• 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 qs and gs roam
  freely
• The QCD vacuum ground-state of QCD
• has a complicated structure
• contains scalar and vector condensates
• explore vacuum-structure by heating/melting QCD
  matter
• Quark-Gluon-Plasma

5
2004 Nobel Prize in Physics
6
Phases of Normal Matter
solid
liquid
gas

• electromagnetic interactions determine phase
  structure of normal matter

7
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!

8
QCD on the Lattice

• Goal explore the thermodynamics of QCD
• evaluate QCD partition function
• path integral with N steps in imaginary time
• can be numerically calculated on a 4D Lattice

Equation of State for an ideal QGP
(ultra-relativistic gas of massless bosons)

• LGT predicts a phase-transition to a state of
  deconfined nearly massless quarks and gluons
• QCD becomes simple at high temperature and/or
  density

F. Karsch
9
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

10
Telescope for the Early Universe The
Relativistic Heavy-Ion Collider
11
Brookhaven National Laboratory
12
Detectors at RHIC

• solenoid as centerpiece
• total detector weight 1200 tons
• TPC tracking of 1000s of particles
  simultaneously
• can record dozens AuAu collisions per second

• Example STAR Detector
• 52 institutions, 12 countries
• 529 collaborators
• construction cost 80 M

13
Collisions at RHIC

• typical collision recorded by the STAR
  detector AuAu _at_ 200 GeV/NN-pair
• 1000s of tracks have to be reconstructed to
  determine species and momenta of produced hadrons
  and characterize collision

14
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 AuAu at
  RHIC - S. A. Bass, B. Mueller and D.K.
  Srivastava, Phys. Lett. B551 (2003) 277

15
Time-Evolution of a Heavy-Ion Collision
16
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 dofs
  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

17
Kinetic Theory- formal language of transport
models -
classical approach
Liouvilles Equation

• use BBKGY hierarchy and cut off at 1-body level

a) interaction based only on potentials Vlasov
Equation
b) interaction based only on scattering
Boltzmann Equation
with
18
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
• main parameter
• cross section probability for an interaction to
  take place, which is interpreted geometrically

dmin
19
Applying Transport Theory to Heavy-Ion Collisions
Pb Pb _at_ 160 GeV/nucleon (CERN/SPS)

• calculation done with the UrQMD
  (Ultra-relativistic Quantum Molecular Dynamics)
  model
• initial nucleon-nucleon collisions excite
  color-flux-tubes (chromo-electric 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 gt 1000 hadrons

20

• Recent Discoveries
• the case for the QGP

21

• 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
22
Jet-Quenching Basic Idea
What is a jet?

• partons lose energy and/or fragment differently
  than in the vacuum radiative energy loss
• transport coefficient q is sensitive to density
  of (colored) charges

• fragmentation of hard scattered partons into
  collimated jets of hadrons
• pp reactions provide a calibrated probe, well
  described by pQCD
• what happens if partons traverse a high energy
  density colored medium?

23
q-hat at RHIC

• suppression can be experimentally quantified in
  terms of RAA ratio

• RHIC data shows values for q-hat far larger than
  expected even for a QGP!

24
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

• data show strong hints of mach-cone formation
• angle indicates surprisingly low speed of sound

• J. Casalderrey-Solana, E.V. Shuryak D. Teaney
  Nucl. Phys. A774 (2006) 577
• T. Renk J. Ruppert Phys. Rev. C73 (2006) 011901

25

• intermediate times
• creation of an ideal liquid
• (anomalous) viscosity

• 1999 first hybrid with 11D hydro
• won LBNL/INT RHIC predictions prize
• 100 citations
• 2006 first full 3D hydro implementation

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
26
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?

27
Relativistic Fluid Dynamics (RFD)

• transport of macroscopic degrees of freedom
• based on conservation laws ?µTµ?0 ?µjµ0
• for ideal fluid Tµ? (ep) uµ u? - p gµ? and
  jiµ ?i uµ
• Equation of State needed to close system of
  PDEs pp(T,?i)
• 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

28
Collision Geometry Elliptic Flow

• two nuclei collide rarely head-on, but mostly
  with an offset

only matter in the overlap area gets compressed
and heated up

• 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

29
Elliptic flow early creation
P. Kolb, J. Sollfrank and U.Heinz, PRC 62 (2000)
054909
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.
30
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!

K. M. OHara, S. L. Hemmer, M. E. Gehm, S. R.
Granade, J. E. Thomas Science 298 (2002) 2179
31
Viscosity 101
shear and bulk viscosity are defined as the
coefficients in the expansion of the stress
tensor in terms of the velocity fields
assuming matter to be quasi-particulate in nature

• viscosity decreases with increasing cross
  section (forget molasses!!)
• for RFD, the microscopic origin of the viscosity
  is not important

32
Viscosity at RHIC
large elliptic flow success of ideal
RFD zero/small viscosity
expanding hadron gas w/ significant
increasing mean free path large viscosity

• viscosity of matter _at_ RHIC changes strongly with
  time phase
• ideal RFD breaks down in later reaction stages
• need to take viscous corrections for hadron gas
  into account

33
3D-Hydro UrQMD Model

• Full 3-d Hydrodynamics
• QGP evolution

UrQMD
Hadronization
Cooper-Frye formula
hadronic rescattering
Monte Carlo
t fm/c
TC
TSW
Hydrodynamics micro. transport (UrQMD)

• ideally suited for dense systems
• model early QGP reaction stage
• well defined Equation of State
• parameters
• initial conditions
• Equation of State

• 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

34
3D-HydroUrQMD Results

• good agreement with wide variety of data
• HU to date the most successful description for
  bulk matter _at_ RHIC
• confirms very low viscosity of matter in the QGP
  phase

35
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
36
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

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

• in all theories with gravity duals one finds
  (?very small number!)

• caution
• N4 SUSY YM is not QCD
• no information on how low ?/s is microscopically
  generated

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
37
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 ??0.1 fm (close to uncertainty bound)
  dissipative effects are large
• gluon densities needed for jet-quenching
  calculations may be too large compared to
  measured entropy

D. Molnar

• does a small viscosity have to imply that matter
  is strongly interacting?
• Paradigm shift needed consider effects of
  (turbulent) color fields

38
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 _at_ 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.

39
Weibel (two-stream) instability

• Ultra-Relativistic Heavy-Ion Collision two
  streams of colliding color charges
• consider the effect of a seed magnetic field with

• 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.
40
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

• for any anisotropic momentum distribution 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)
41
Anomalous vs. Collisional Viscosity

• collisional viscosity
• derived in HTL weak coupling limit
• anomalous viscosity
• induced by turbulent color fields, due to
  momentum-space anisotropy
• Note that for reasonably small values in the
  coupling

42
Collisional vs. Anomalous Viscosity
temperature evolution

• cross sections are additive
• ???f?1/s
• sumrule for viscosities

• 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!

43

• Dynamics of Hadronization
• The baryon puzzle at RHIC
• Recombination Fragmentation Model
• quark-number scaling of elliptic flow

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
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
44
The baryon puzzle _at_ RHIC

• species dependence of v2 saturation
• not predicted by RFD
• why do baryons overtake mesons?

• why do protons not exhibit the same jet-
  suppression as pions?
• fragmentation starts with a single fast parton
  energy loss affects pions and protons in the same
  way!

v2
45
RecombinationFragmentation Model

• basic assumptions
• at low pt, the quarks and antiquark spectrum is
  thermal and they recombine into hadrons locally
  at an instant
• 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
  quarks and gluons

• 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!

46
Reco Single Particle Observables

• consistent description of spectra, ratios and RAA

47
Parton Number Scaling of v2

• in leading order of v2, recombination predicts

• smoking gun for recombination
• measurement of partonic v2 !

Most direct deconfinement signature to date!
48
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

49
Summary and Conclusion

• Heavy-Ion collisions at RHIC have produced a
  deconfined state of matter which can be called a
  Quark-Gluon-Plasma
• the QGP has the properties of a near ideal fluid
  with a (very) small viscosity
• (turbulent) color fields induce an anomalous
  viscosity, which keeps the total shear-viscosity
  small during the QGP evolution
• parton recombination shows direct evidence for
  the built-up of collectivity in the deconfined
  phase

• QGP research utilizes
• insights from
• QCD
• Lattice field theory
• kinetic/transport theory
• statistical mechanics
• fluid dynamics
• plasma physics
• string theory
• AMO Fermi-systems

• Note
• due to its slow nearly isotropic expansion, the
  early Universe most likely did not have an
  anomalous contribution to its viscosity

50
The End
51
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
• Youre doing physics at RHIC!

52
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

RF Cavity system
53
Initial Particle Production in UrQMD
54
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 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
55
?/s bound in QCD from AdS/CFT

• viscosity from Kubos formula

• AdS/CFT correspondence
• Imaginary part of retarded Greensfunction
• is mapped on graviton absorption cross section
• viscosity ? graviton absorption cross section
• absorption cross section area of horizon A
• entropy SA/4G
• in all theories with gravity duals one finds
  (?very small number!)

• caution
• N4 SUSY YM is not QCD
• no information on how low ?/s is microscopically
  generated

56
The RHIC Transport Initiative
Duke Univ. Ohio State Michigan State Purdue
U. of Minnesota
57
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
Effective HTL theory permits systematic study of
instabilities of soft color fields

• find HTL modes for anisotropic distribution
• for any ??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)
58
Anomalous Viscosity Derivation Sketch

• linear Response connect ? with momentum
  anisotropy ?
• use color Vlasov-Boltzmann Eqn. to solve for f
  and ?
• Turbulent color field assumption
• ensemble average over fields
• diffusive Vlasov-Boltzmann Eqn
• example anomalous viscosity in case of
  transverse magnetic fields