Probing the QGP at RHIC

1
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)

2
Time-Evolution of a Heavy-Ion Collision
3
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
(F. Karsch, hep-lat/0106019)
(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

4

• high-pt and early times
• manifestations of pre-equilibrium
• jet production and quenching
• photons leptons

5
Jet-Quenching Basic Idea
What is a jet?

• partons can loose energy and/or fragment
  differently than in the vacuum
• energy loss can be quantified
• partons probe the deconfined medium, 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?

I. Vitev, QM04
(static)
(Bjorken)
6
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
• 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
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Jet-Medium Interactions

• how does a fast moving color charge influence the
  medium it is traversing?
• can Mach-shockwaves be created?
• information on plasmas properties is contained
  in longitudinal and transverse components of the
  dielectricity tensor
• two scenarios of interest
• High temperature pQCD plasma
• 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

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Wakes in the QCD Medium

• High temperature pQCD plasma
• Calculation in HTL approximation
• color charge density wake is a co-moving
  screening cloud
• Strongly coupled quantum liquid (sQGP)
• subsonic jet analogous results to pQCD plasma
  case
• supersonic jet emission of plasma oscillations
  with Mach cone emission angle ?Farccos(u/v) v
  parton velocity, u plasmon propag. velocity

J. Ruppert B. Mueller, Phys. Lett. B618 (2005)
123
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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)

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• 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

11

• low-pt and intermediate times
• creation and evolution of the QGP
• Hydrodynamics and anisotropic flow
• Thermalization

12
Collision Geometry Elliptic Flow

• 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

• 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

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Nuclear Fluid Dynamics

• 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 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

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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.
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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!

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Matter at RHIC nearly ideal fluid?
K and p ratio normalized to T160 MeV!

• Hydrodynamic initial conditions
• thermalization time t0.6 fm/c and e20 GeV/fm3

C. Nonaka SAB
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The not-so-perfect Fluid

• Ideal Hydrodynamics (Heinz, Kolb Sollfrank
  Hirano, Huovinen,)
• assumes vanishing mean free path ?, 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/
  ?s and Os)
• 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 ? species-independent
  cross section still hold
• Hybrid HydroMicro 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

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3D-HydroMicro first results

• C. Nonaka S.A. Bass
• 3D-HydroUrQMD

• first fully 3-dimesional HydroMicro 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/d?
• large effect due to resonance decays

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Connecting high-pt partons with the dynamics of
an expanding QGP

• Jet quenching analysis taking
• account of (21)D hydro results
• (M.Gyulassy et al. 02)

hydrojet model
color QGP fluid density symbols mini-jets
HydroJet model T.Hirano. Y.Nara Phys.Rev.C66
041901, 2002
y

• use GLV 1st order formula for parton
• energy loss (M.Gyulassy et al. 00)

AuAu 200AGeV, b8 fm transverse
plane_at_midrapidity Fragmentation switched off
x

• take Parton density ?(x) from full 3D
  hydrodynamic calculation

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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!?!

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• 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
• HydroMicro can alleviate many Hydro shortcomings
• Challenges
• transport coefficients (e.g. viscosity)
• HOW DID THE SYSTEM THERMALIZE?? (need
  experimentally verifiable/falsifiable concepts)

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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
• an interaction takes place if at the time of
  closest approach dmin of two partons
• 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

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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!!

T. Renk SAB
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Equilibration II v2 as indicator

• run binary collision PCM and compare to hydro-
  dynamics with identical initial conditions
• even for sparton a factor of 10-15 above spQCD,
  the hydro limit is not obtained!
• strong dissipative effects

D. Molnar P. Huovinen, Phys.Rev.Lett.94012302,
2005

• Lesson
• perturbative processes seem insufficient for
  thermalization
• Caution
• role of multi-particle interactions still under
  debate (Greiner Xu)

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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)

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• 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

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The baryon puzzle _at_ 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/Npltlt1
• fragmentation starts with a single fast parton
  energy loss affects pions and protons in the same
  way!

v2
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RecombinationFragmentation Model

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

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Reco Single Particle Observables

• consistent description of spectra, ratios and RAA

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Parton Number Scaling of v2

• in leading order of v2, recombination predicts

note that scaling breaks down in the
fragmentation domain

• smoking gun for recombination
• measurement of partonic v2 !

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• 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

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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
• clear jet-like structure observed at
• intermediate pT
• very similar to pp jet fragmentation?
• analyze as function of integrated yield
• simple recombination of uncorrelated
  thermal quarks cannot reproduce two
  particle correlations

33
Recombination Inclusion of Correlations

• Recombination approach allows for two particle
  correlations, provided they are contained in the
  parton source distributions
• Which results in a correlated two hadron yield

34
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

• 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?(pTC)2?0.5 GeV2 degrees of
  freedom likely dominated by lowest Fock state
  (i.e. valence quark state)

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Higher Fock States v2 Scaling Violations

• Generalization of scaling law to higher Fock
  states
• assume all partons carry roughly equal momentum
  xi?1/n?
• with n? the number of partons in the Fock
  state
• valence quark approximation ?1, n12,3 and C11
• (scaled v2 identical to parton v2)
• general result

• scaling violations ? 5

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• 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

37
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 dont
  forget the big picture in the process!!

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The End
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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
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Lattice current status

• technical progress finer mesh size, physical
  quark masses, improved fermion actions
• phase-transition smooth, rapid cross-over
• critical temperature TC?1939 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