Probing the QGP at RHIC:
Lessons and Challenges
Steffen A. Bass
Duke University
• Jet-Medium Interactions
• Hydro and beyond
• Recombination
Topics not covered due to lack of time:
• Photons
• Dileptons
• Charm(onium)
Steffen A. Bass
Probing the QGP at RHIC #1
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
Probing the QGP at RHIC #2
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:
(F. Karsch, hep-lat/0106019)
  30 gDOFT
2
4
(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
Steffen A. Bass
Probing the QGP at RHIC #3
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
high-pt and early times:
manifestations of pre-equilibrium
• jet production and quenching
• [photons & leptons]
Steffen A. Bass
Probing the QGP at RHIC #4
Jet-Quenching: Basic Idea
What is a jet?
leading
particle
hadrons
leading
particle
suppressed
hadrons
q
q
q
q
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
hadrons
leading
particle
suppressed
• partons can loose energy and/or fragment
differently than in the vacuum
• energy loss can be quantified:
I. Vitev, QM04
CR s  2 L2
 2E 
E 
log  2   ... (static)
4
g
 L
9 CR s3
 2E 
1 dN g
E 
L
log  2   ... (Bjorken)
4
A dy
 L
 partons probe the deconfined medium,
sensitive to density of (colored) charges
Probing the QGP at RHIC #5
Jet-Quenching: direct jet correlation
• establish near-side (trigger-jet) and
far-side (counter-jet) correlation in pp
• ansatz: correlation in AA as
superposition of pp signal and elliptic
flow
– pp signal from pp data
– elliptic flow from reaction plane
analysis
C2 ( Au  Au )  C2 ( p  p )
 A  (1  2v22 cos(2 ))
• back-to-back correlation disappears in
central AuAu
 surface emission for near-side jets
 quenching of far-side jets
Steffen A. Bass
D. Hardtke, STAR plenary talk QM02
Probing the QGP at RHIC #6
Jet-Medium Interactions
•
•
how does a fast moving color charge
influence the medium it is traversing?
can Mach-shockwaves be created?
 information on plasma’s properties is
contained in longitudinal and transverse
components of the dielectricity tensor
two scenarios of interest:
1. High temperature pQCD plasma
2. Strongly coupled quantum liquid (sQGP)
Steffen A. Bass
•
•
•
H. Stoecker, Nucl. Phys. A750 (2005) 121
J. Ruppert & B. Mueller, Phys. Lett. B618 (2005) 123
J. Casalderrey-Solana, E.V. Shuryak, D. Teaney, hep-ph/0411315
Probing the QGP at RHIC #7
Wakes in the QCD Medium
1. High temperature pQCD plasma:
•
•
Calculation in HTL approximation
color charge density wake is a co-moving screening cloud
2. Strongly coupled quantum liquid (sQGP):
•
•
subsonic jet: analogous results to pQCD plasma case
supersonic jet: emission of plasma oscillations with Mach cone emission
angle: ΔΦ=arccos(u/v) [v: parton velocity, u: plasmon propag. velocity]
J. Ruppert & B. Mueller,
Phys. Lett. B618 (2005) 123
Steffen A. Bass
Probing the QGP at RHIC #8
Jet-Medium Interactions: Observables
T. Renk & J. Ruppert
hep-ph/0509036
• in the sQGP scenario, Mach
cones lead to a directed
emission of secondary partons
from the plasma
 creation and propagation of a
sound wave
 visible in away-side jet angular
correlation function
 emission angle & shape of correlation function is sensitive to:
• QGP equation of state
• speed of sound
• fraction of jet-energy deposited into collective excitation
• Question: nature of the Mach cone angular correlation? (2/3/n-body…)
Steffen A. Bass
Probing the QGP at RHIC #9
Lessons:
• Jet-quenching well established as final state effect
 probes gluon density of medium
 color-wake phenomena (if confirmed!) provide
novel & more detailed insights into medium
properties
Challenges:
• verification/falsification of color-wake phenomena
• quantitative characterization of medium properties
Steffen A. Bass
Probing the QGP at RHIC #10
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
low-pt and intermediate times:
creation and evolution of the QGP
• Hydrodynamics and anisotropic flow
• Thermalization
Steffen A. Bass
Probing the QGP at RHIC #11
Collision Geometry: Elliptic Flow
Reaction
plane
z
 The application of fluid-dynamics
implies 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
Probing the QGP at RHIC #12
Nuclear 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
• simplest case: scaling hydrodynamics
–
–
–
–
assume longitudinal boost-invariance
cylindrically symmetric transverse expansion
no pressure between rapidity slices
conserved charge in each slice
Steffen A. Bass
Probing the QGP at RHIC #13
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
Probing the QGP at RHIC #14
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
Probing the QGP at RHIC #15
Matter at RHIC: nearly ideal fluid?
K and p ratio normalized to
T=160 MeV!
b=4.5 fm
b=6.3
Hydrodynamic initial conditions:
• thermalization time t=0.6 fm/c and ε=20 GeV/fm3
Steffen A. Bass
C. Nonaka & SAB
Probing the QGP at RHIC #16
The not-so-perfect Fluid
Ideal Hydrodynamics: (Heinz, Kolb & Sollfrank; Hirano, Huovinen,…)
• assumes vanishing mean free path λ, even in the dilute, break-up phase
 fails to describe protons & pions simultaneously w/o rescaling, due to
chemical and kinetic freeze-out being identical
 no species-dependent cross sections (problem w/ Ξ’s and Ω’s)
Ideal Hydrodynamics with Partial Chemical Equilibrium:
(Hirano & Tsuda, Kolb & Rapp, Teaney)
• separates chemical from kinetic freeze-out
 successful for simultaneously describing proton, kaon & pion spectra
 assumptions of vanishing λ & species-independent cross section still hold
Hybrid Hydro+Micro Approach:
(SAB & Dumitru; Teaney, Lauret & Shuryak; Hirano & Nara, Nonaka & SAB)
• self-consistent calculation of freeze-out with finite mean free path and
species-dependent cross section
• full treatment of viscous effects in hadronic phase
Steffen A. Bass
Probing the QGP at RHIC #17
3D-Hydro+Micro: first results
C. Nonaka & S.A. Bass
3D-Hydro+UrQMD
Steffen A. Bass
• first fully 3-dimesional Hydro+Micro calc.
• microscopic calculation of hadronic phase:
 selfconsistent treatment of freeze-out
 inclusion of viscous effects
 good agreement with spectra below 1.5 GeV
 reproduces centrality dependence of dN/dη
 large effect due to resonance decays
Probing the QGP at RHIC #18
Connecting high-pt partons with the
dynamics of an expanding QGP
• Jet quenching analysis taking
hydro+jet model
account of (2+1)D hydro results
(M.Gyulassy et al. ’02)
color: QGP fluid density
symbols: mini-jets
Hydro+Jet model
use GLV 1st order formula for parton
energy loss (M.Gyulassy et al. ’00)

y
T.Hirano. & Y.Nara: Phys.Rev.C66 041901, 2002
Au+Au 200AGeV, b=8 fm
transverse plane@midrapidity
Fragmentation switched off
take Parton density ρ(x) from
full 3D hydrodynamic calculation
Steffen A. Bass
x
Probing the QGP at RHIC #19
Strangeness & Charm:
Thermalization &Recombination
• multi-strange baryons follow same v2 scaling as hyperons & protons
 strange quarks equilibrate and flow the same way as light quarks!
 indications that D-mesons exhibit same trend: charm equilibration!?!
Steffen A. Bass
Probing the QGP at RHIC #20
Lessons:
• system acts in 1st approx like a near ideal fluid
• heavy quarks might thermalize as well
• initial conditions well in the realm of deconfinement
as predicted by lQCD
• Hydro+Micro can alleviate many Hydro shortcomings
Challenges:
• transport coefficients (e.g. viscosity)
• HOW DID THE SYSTEM THERMALIZE??
(need experimentally verifiable/falsifiable concepts)
Steffen A. Bass
Probing the QGP at RHIC #21
The Parton Cascade Model (PCM)
Goal: provide a microscopic space-time description of
relativistic heavy-ion collisions based on perturbative QCD
• degrees of freedom: quarks and gluons
• solve a Boltzmann Transport-Equation:
 p  1
 t  m  r  f  N   d  dp2 v1  v2  f1 ( p1) f1 ( p2 )  f1 ( p1 ) f1 ( p2 ) 
• an interaction takes place if at the time of closest approach dmin of two

partons

d sˆ ; p1 , p2 , p3 , p4
 tot
dtˆ
d min   with  tot  p, p 
dtˆ
• system evolves through a sequence of binary (22) elastic and
inelastic scatterings of partons and (optional) initial and final state
radiations within a leading-logarithmic approximation (2N)
• binary cross sections are calculated in leading order pQCD with either
a momentum cut-off or Debye screening to regularize IR behavior
• guiding scales: initialization scale Q0, pT cut-off p0 / Debye-mass μD
3
Steffen A. Bass
4
Probing the QGP at RHIC #22
Equilibration I: Infinite Matter
• run PCM in a box with periodic
boundary conditions:
 kinetic and chemical
equilibration
 relaxation times
 Equation of State
• box mode with 2-2 scattering:
 proper thermal and chemical
equilibrium obtained
 chemical equilibration time
~2500 fm/c!!
Steffen A. Bass
T. Renk & SAB
Probing the QGP at RHIC #23
Equilibration II: v2 as indicator
• run binary collision PCM and
compare to hydro- dynamics
with identical initial
conditions
 even for σparton a factor of
10-15 above σpQCD, the
hydro limit is not obtained!
 strong dissipative effects
Lesson:
D. Molnar & P. Huovinen,
Phys.Rev.Lett.94:012302,2005
• perturbative processes seem insufficient for thermalization
Caution:
• role of multi-particle interactions still under debate (Greiner & Xu)
Steffen A. Bass
Probing the QGP at RHIC #24
Non-Perturbative Models for
Thermalization
 requires microscopic transport & progress on transport
coefficients
A selection of current ideas:
• Plasma Instabilities (Mrowczynski, Lenaghan & Arnold; Strickland;
Dumitru & Nara)
•
•
•
•
Heavy-quark EFT (van Hees & Rapp)
Classical fields + particle degrees of freedom (Molnar)
Brueckner-type many-body calculations (Mannarelli & Rapp)
Critical opacity at the phase transition (Aichelin & Gastineau)
Steffen A. Bass
Probing the QGP at RHIC #25
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
Intermediate-pt and late(r) times:
dynamics of hadronization
 Recombination & Fragmentation
•
•
•
•
The baryon puzzle at RHIC
Recombination + Fragmentation Model
Results: spectra, ratios and elliptic flow
Challenges: correlations, entropy balance & gluons
Steffen A. Bass
Probing the QGP at RHIC #26
The baryon puzzle @ RHIC
• where does the large proton over pion
ratio at high pt come from?
• why do protons not exhibit the same
jet- suppression as pions?
• species dependence of v2 saturation?
 fragmentation yields Np/Nπ<<1
 fragmentation starts with a single fast
parton: energy loss affects pions and
protons in the same way!
v2
Steffen A. Bass
Probing the QGP at RHIC #27
Recombination+Fragmentation Model
basic assumptions:
• at low pt, the quarks and antiquark spectrum is thermal and
they recombine into hadrons locally “at an instant”:
qq  M
qqq  B
 features of the parton spectrum are shifted to higher pt in
the hadron spectrum
• 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
• shape of parton spectrum
determines if recombination is more
effective than fragmentation
• baryons are shifted to higher pt
than mesons, for same quark
distribution
 understand behavior of baryons!
Steffen A. Bass
Probing the QGP at RHIC #28
Reco: Single Particle Observables
 consistent description of spectra, ratios and RAA
Steffen A. Bass
Probing the QGP at RHIC #29
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
note that scaling
breaks down in the
fragmentation domain
Probing the QGP at RHIC #30
Lessons:
• reco success for single-particle distributions & v2
indicates formation of hadrons from a system of
deconfined quarks at TC (sQGP?)
Challenges:
• dynamical two-particle correlations
• treatment of gluons & sea-quarks
 R.J. Fries, S.A. Bass & B. Mueller, PRL 94 122301 (2005)
 C. Nonaka, B. Mueller, S.A. Bass & M. Asakawa, PRC 71 051901 (2005) Rapid C.
 B. Mueller, S.A. Bass & R.J. Fries, Phys. Lett. B in print, nucl-th/0503003
Steffen A. Bass
Probing the QGP at RHIC #31
Two-Particle Correlations
• PHENIX & STAR measure associated yields in pT windows of a few GeV/c.
• trigger hadron A, associated hadron B: associated yield as a function of
relative azimuthal angle
1  dN AB d ( N A N B ) 
YAB    



N A  d ( )
d ( ) 
 clear jet-like structure observed at
intermediate pT
 very similar to p+p; jet fragmentation?
• analyze as function of integrated yield:
0.94
cone
YAB

 d    Y   
AB
0
 simple recombination of uncorrelated
thermal quarks cannot reproduce two
particle correlations
Steffen A. Bass
Probing the QGP at RHIC #32
Recombination: Inclusion of Correlations
• Recombination approach allows for two particle
correlations, provided they are contained in the
parton source distributions:
W1234


 w1w2 w3 w4 1   Cij 
 i j 
 Which results in a correlated two hadron yield:
d 6 N AB
 C AB  d A d B  A   B  W1234
3
3
d PA d PB

Steffen A. Bass
Probing the QGP at RHIC #33
Thermal Recombination beyond the
Valence Quark Approximation
 investigate effects of more sophisticated internal hadron structure
• use light-cone frame
• write hadron wavefunction as expansion in terms of Fock-States:
M   dxa dxb   xa  xb  1 c1  xa , xb  q  xa  q  xb 
1
0
  dxa dxb dxc   xa  xb  xc  1 c2  xa , xb , xc  q  xa  q  xb  g  xc 
1
0
  dxa dxb dxc dxd   xa  xb  xc  xd  1 c3  xa , xb , xc , xd  q  xa  q  xb  q  xc  q  xd  
1
0
General Result:
(B. Mueller, R.J. Fries & SAB, Phys. Lett. B618 (2005) 77)
 in the Boltzmann approximation the emission probability of a complex
state from a thermal ensemble is independent of degree of complexity of
the structure of the state
• note that for Q2(πTC)20.5 GeV2 degrees of freedom likely dominated by
lowest Fock state (i.e. valence quark state)
Steffen A. Bass
Probing the QGP at RHIC #34
Higher Fock States: v2 Scaling Violations
Generalization of scaling law to higher Fock states:
• assume all partons carry roughly equal momentum xi1/nν
with nν the number of partons in the Fock state
v2( H )  P    C n v2  P / n 

• valence quark approximation: ν=1, n1=2,3 and C1=1
v2( M )  p   v2( B)  p   v2  p 
(scaled v2 identical to parton v2)
 general result:
v2( M )  p    C( M )

(B)
2
v
 p    C
(B)

Steffen A. Bass
n( M )
v2  2 p / n( M ) 
2
n( B )
v2  3 p / n( B ) 
3
 scaling violations  5%
P. Sorensen, QM05
Probing the QGP at RHIC #35
Lessons:
• dynamical correlations compatible with reco approach
• inclusion of gluons & sea-quarks: interpretation of
scaled v2 as partonic flow still valid
Beware:
• Recombination is not a dynamical model for the
time-evolution of a heavy-ion reaction, but only a
formalism on how to hadronize an ensemble of
constituent quarks
 snapshot of system at TC
Steffen A. Bass
Probing the QGP at RHIC #36
Last Words…
• The (s)QGP has been discovered – the gunsmoke
is thickening w/ every measurement!
• RHIC experiments have performed way beyond
expectations!
• RHIC physics is transitioning from the discovery
phase to the exploratory phase:
 keep pushing the envelope w/ new measurements!
 do not neglect the nitty-gritty details – they will
become more important in quantitatively determining the
sQGP properties… - but don’t forget the big picture in
the process!!
Steffen A. Bass
Probing the QGP at RHIC #37
The End
Steffen A. Bass
Probing the QGP at RHIC #38
Lattice: current status
• technical progress: finer mesh size, physical quark masses, improved
fermion actions
 phase-transition: smooth, rapid cross-over
 EoS at finite μB: in reach, but with large systematic uncertainties
 critical temperature: TC180 MeV
Fodor & Katz, hep-lat/0110102
Rajagopal & Wilczek, hep-ph/0011333
Steffen A. Bass
Probing the QGP at RHIC #39
Lattice: current status
• technical progress: finer mesh size, physical quark masses, improved
fermion actions
 phase-transition: smooth, rapid cross-over
 critical temperature: TC193±9 MeV
 EoS at finite μB: large systematic uncertainties
Beware:
• current estimate for TC significantly higher than previous estimates!
• implications for interpretation of
Statistical Model fits to hadron
ratios:
 difference between Tch and TC
implies evolution of hadronic
matter in chemical equilibrium
 experimental determination of TC
problematic
Steffen A. Bass
Probing the QGP at RHIC #40