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.
Download ReportTranscript 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.
Probing the QGP at RHIC: Lessons and Challenges
Steffen A. Bass
Duke University • Jet-Medium Interactions • Hydro and beyond • Recombination
Steffen A. Bass Topics not covered due to lack of time: • Photons • Dileptons • Charm(onium) Probing the QGP at RHIC #1
Time-Evolution of a Heavy-Ion Collision
QGP and hydrodynamic expansion hadronic phase and freeze-out initial state pre-equilibrium hadronization Lattice-Gauge Theory: Experiments: Transport-Models & Phenomenology:
• rigorous calculation of QCD quantities • works in the infinite size / equilibrium limit • observe the final state + penetrating probes • rely on QGP signatures predicted by Theory • full description of collision dynamics • 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 n e
H n
, 1 , ,
n N n e
H n
1
n e
1 path integral with N steps in imaginary time
H
can be numerically calculated on a 4D Lattice (F. Karsch, hep-lat/0106019)
n
2
n e N
H n
Equation of State for an ideal QGP: 2
g T
4 30 DOF (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 QGP and hydrodynamic expansion hadronic phase and freeze-out pre-equilibrium hadronization
high-p
t
and early times: manifestations of pre-equilibrium
• jet production and quenching • [photons & leptons]
Steffen A. Bass Probing the QGP at RHIC #4
What is a jet?
hadrons q
Jet-Quenching: Basic Idea
leading particle leading particle suppressed hadrons 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
q hadrons
•
leading particle suppressed
partons can loose energy and/or fragment differently than in the vacuum • energy loss can be quantified: I. Vitev, QM04
C R
4
s
2
g L
2 log 2 E 2
L
...
(static) 9 4
R s
3
L
1
A
d N dy g
log 2 E 2
L
...
(Bjorken) 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 2 ( ) 2 ( )
v
2 )) 2 • back-to-back correlation disappears in central AuAu surface emission for near-side jets quenching of far-side jets D. Hardtke, STAR plenary talk QM02 Steffen A. Bass Probing the QGP at RHIC #6
Steffen A. Bass
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) 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] Steffen A. Bass J. Ruppert & B. Mueller, Phys. Lett. B618 (2005) 123 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 QGP and hydrodynamic expansion hadronic phase and freeze-out pre-equilibrium hadronization
low-p
t
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 (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 Steffen A. Bass Probing the QGP at RHIC #12
Nuclear 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 • Equation of State needed to close system of PDE’s: connection to Lattice QCD calculation of EoS = ρ i u μ p=p(T,ρ i ) • 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 ultra relativistic 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!
Hydrodynamic initial conditions: • thermalization time t=0.6 fm/c and ε=20 GeV/fm 3 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-p
t
partons with the dynamics of an expanding QGP
• Jet quenching analysis taking account of (2+1)D hydro results (M.Gyulassy et al. ’02)
hydro+jet model color: QGP fluid density symbols: mini-jets Hydro+Jet model
T.Hirano. & Y.Nara: Phys.Rev.C66 041901, 2002 use GLV 1 st order formula for parton energy loss (M.Gyulassy et al. ’00) Au+Au 200 A GeV, b =8 fm transverse plane@midrapidity Fragmentation switched off
x
take Parton density ρ ( x ) from full 3D hydrodynamic calculation Steffen A. Bass Probing the QGP at RHIC #19
Strangeness & Charm: Thermalization &Recombination
• multi-strange baryons follow same v 2 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 1 st 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:
t m d r
f
1
N
d d
p v
2 1
v
2 1 ( 1 ) ( 1 2 ) 1 ( 1 ) ( 1 2 ) • an interaction takes place if at the time of closest approach partons radiations min
tot
inelastic scatterings with
tot
, 4
d
ˆ; , , , 1 2 3 4
dt
ˆ of partons and (optional)
dt
ˆ within a leading-logarithmic approximation (2 N) d min • system evolves through a sequence of binary (2 2) elastic and of two initial and final state • binary cross sections are calculated in leading order pQCD with either a momentum cut-off or Debye screening to regularize IR behavior • guiding scales: Steffen A. Bass initialization scale Q 0 , p T cut-off p 0 / Debye-mass μ D
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: v
2
as indicator
• run binary collision PCM and compare to hydro- dynamics with identical initial conditions even for σ parton a factor of 10-15 above σ pQCD , 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 QGP and hydrodynamic expansion hadronic phase and freeze-out pre-equilibrium hadronization
Intermediate-p
t
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
Steffen A. Bass
The baryon puzzle @ RHIC
• where does the large proton over pion ratio at high p t come from?
• why do protons not exhibit the same jet- suppression as pions?
• species dependence of v 2 saturation?
fragmentation yields N p /N π <<1 fragmentation starts with a single fast parton: energy loss affects pions and protons in the same way!
v 2 Probing the QGP at RHIC #27
Recombination+Fragmentation Model
basic assumptions: • at low p t , the quarks and antiquark spectrum is thermal and they recombine into hadrons locally “at an instant”:
M qqq
B
features of the parton spectrum are shifted to higher p t the hadron spectrum in • at high p t , 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 Steffen A. Bass • shape of parton spectrum determines if recombination is more effective than fragmentation • baryons are shifted to higher p t than mesons, for same quark distribution understand behavior of baryons!
Probing the QGP at RHIC #28
Reco: Single Particle Observables
consistent description of spectra, ratios and R AA Steffen A. Bass Probing the QGP at RHIC #29
Parton Number Scaling of v
2
v
•in leading order of v 2 , recombination predicts: 2
v
2
p p t v
2 2
M M
and
t
v
2
p
2 2
p t
2
v
2
p
2
t
v
2
B v
2
B
t
3
v
2
p
p t
3 3
v v
2
p
2 3
p
p t v
2
p
3
p
3
p t
2
t
3 3 smoking gun for recombination measurement of partonic v 2 !
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 & v deconfined quarks at T C (sQGP?) 2 indicates formation of hadrons from a system of
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 p T windows of a few GeV/c.
• trigger hadron A, associated hadron B: associated yield as a function of relative azimuthal angle
Y AB
N
1
A
d dN
(
AB
)
d
(
A
)
B
) clear jet-like structure observed at intermediate p T very similar to p+p; jet fragmentation?
• analyze as function of integrated yield: cone
Y AB
0.94
0
d
AB
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:
W
1234
w
1
w
2
w
3
w
4 1
C ij
Which results in a correlated two hadron yield:
d
6
N A B
3
A
3
d P d P B
C A B
d
A d
B
A
B
W
1234 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
1 0
dx dx a b
x a
x b
1
a
,
b
0 1
dx dx dx a b c
x a
x b
c
1
a b
,
c
q
0 1
dx dx dx dx a b c d
x a
x b x d
1
a b
,
c
,
d
q
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 Q 2 (πT C ) 2 0.5 GeV 2 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: v
2
Scaling Violations
Generalization of scaling law to higher Fock states: • assume all partons carry roughly equal momentum x i 1/n ν with n ν
v
( 2
H
) the number of partons in the Fock state
P
C n v
2 / • valence quark approximation: ν=1, n 1 =2,3 and C 1 =1
v
2 (
M
)
v
2
v
2 (scaled v2 identical to parton v2) general result:
v
2 (
M
)
C
(
M
)
n
(
M
)
v
2 2
v
2
C
Steffen A. Bass
n
3
v
2 (
M
) 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 v 2 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 T C 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
Steffen A. Bass
The End
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 μ B : in reach, but with large systematic uncertainties critical temperature: T C 180 MeV Fodor & Katz, hep-lat/0110102 Steffen A. Bass Rajagopal & Wilczek, hep-ph/0011333 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: T C 193±9 MeV EoS at finite μ B : large systematic uncertainties Beware: • current estimate for T ratios: C significantly higher than previous estimates!
• implications for interpretation of Statistical Model fits to hadron difference between T ch and T C implies evolution of hadronic matter in chemical equilibrium experimental determination of T C problematic Steffen A. Bass Probing the QGP at RHIC #40