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”: 

qq



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