steffen a. bassprobing the qgp at rhic #1 steffen a. bass duke university probing the qgp at rhic:...

Steffen A. Bass Probing the QGP at RHIC #1

Steffen A. Bass

Duke University

Probing the QGP at RHIC: Lessons and

Challenges

Probing the QGP at RHIC: Lessons and

Challenges

• Jet-Medium Interactions• Hydro and beyond• Recombination

Topics not covered due to lack of time:• Photons• Dileptons• Charm(onium)


Time-Evolution of a Heavy-Ion Collision

Time-Evolution of a Heavy-Ion Collision

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

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 & Phenomenology:

• full description of collision dynamics• connects intermediate state to observables• provides link between LGT and data


QCD on the Lattice

QCD on the Lattice

1

1 1 2, , , N

H H H HN

n n n n

n e n n e n n e n n e n

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

(F. Karsch, hep-lat/0106019)2 4

DOF30 g T 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


high-pt and early times:

manifestations of pre-equilibrium • jet production and quenching• [photons & leptons]

initial state

pre-equilibrium


hadronization



Jet-Quenching: Basic Idea

Jet-Quenching: Basic Idea

• 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

hadrons

q

q

hadrons

leadingparticle

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?

What is a jet?

hadrons

q

q

hadrons

leadingparticle suppressed

leading particle suppressed

2

2

3

2

2

2Elog ...

4

9 1 2Elog ...

4

s

g

R s g

R L

L

d

C

NL

dyE

L

E

C

A

(static)

(Bjorken)

I. Vitev, QM04


Jet-Quenching: direct jet correlation

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

2 2

22

( ) ( )

(1 2 cos(2 ))

C Au Au C p p

A v

D. Hardtke, STAR plenary talk QM02


Jet-Medium InteractionsJet-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 plasma2. 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


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]

Wakes in the QCD Medium

Wakes in the QCD Medium

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

123


Jet-Medium Interactions: Observables

Jet-Medium Interactions: Observables

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…)

• 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

T. Renk & J. Rupperthep-ph/0509036


Lessons:• Jet-quenching well established as final state

effectprobes 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


low-pt and intermediate times:

creation and evolution of the QGP • Hydrodynamics and anisotropic flow• Thermalization

initial state

pre-equilibrium


hadronization



Collision Geometry: Elliptic Flow

Collision Geometry: Elliptic Flow

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

Reaction plane

x

z

y

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…


Nuclear Fluid Dynamics

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


spatial eccentricity

momentumanisotropy

initial energy density distribution:

Elliptic flow: early creation

Elliptic flow: early creation

time evolution of the energy density:

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.


Elliptic Flow: ultra-cold Fermi-Gas

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!


Matter at RHIC: nearly ideal fluid?

Matter at RHIC: nearly ideal fluid?

Hydrodynamic initial conditions:• thermalization time t=0.6 fm/c and ε=20 GeV/fm3

b=4.5 fmb=6.3 fm

K and p ratio normalized to

T=160 MeV!

C. Nonaka & SAB


The not-so-perfect FluidThe not-so-perfect FluidIdeal 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


3D-Hydro+Micro: first results

3D-Hydro+Micro: first results

• 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

C. Nonaka & S.A. Bass

3D-Hydro+UrQMD


Connecting high-pt partons with the dynamics of an expanding

QGP

Connecting high-pt partons with the dynamics of an expanding

QGP

color: QGP fluid densitysymbols: mini-jets

Au+Au 200AGeV, b=8 fmtransverse plane@midrapidityFragmentation switched off

hydro+jet model• Jet quenching analysis takingJet quenching analysis takingaccount of (2+1)D hydro resultsaccount of (2+1)D hydro results (M.Gyulassy et al. ’02)(M.Gyulassy et al. ’02)

Hydro+Jet model T.Hirano. & Y.Nara: T.Hirano. & Y.Nara: Phys.Rev.Phys.Rev.C66C66 041901, 2002 041901, 2002

take Parton density take Parton density ρρ((xx) ) from full 3D hydrodynamic from full 3D hydrodynamic calculationcalculation

x

y use GLV 1use GLV 1stst order formula for order formula for parton parton energy loss (M.Gyulassy et al. energy loss (M.Gyulassy et al. ’00)’00)


Strangeness & Charm: Thermalization

&Recombination

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!?!


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)


The Parton Cascade Model (PCM)

The Parton Cascade Model (PCM)

• 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 (22) elastic and inelastic scatterings of partons and (optional) initial and final state radiations within a leading-logarithmic approximation (2N)• 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 4

1 2 3 4

min,

ˆ; , , ,ˆ with

ˆtot

totp p

d s p p p pdt

dtd

Goal: provide a microscopic space-time description of relativistic heavy-ion collisions based on perturbative QCD

12 1 2 1 1 1 2 1 1 1 2d d ( ) ( ) ( ) ( )r

pf N p v v f p f p f p f p

t m


Equilibration I: Infinite Matter

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


Equilibration II: v2 as indicator

Equilibration II: v2 as indicator

• run binary collision PCM and compare to hydrodynamics with identical initial conditions

even for σparton a factor of 10-15 above σpQCD, the hydro limit is not obtained!

strong dissipative effects

Lesson:• perturbative processes seem insufficient for thermalization

Caution:• role of multi-particle interactions still under debate (Greiner & Xu)

D. Molnar & P. Huovinen, Phys.Rev.Lett.94:012302,20

05


Non-Perturbative Models for Thermalization

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)


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

initial state

pre-equilibrium


hadronization



The baryon puzzle @ RHIC

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


Recombination+Fragmentation Model

Recombination+Fragmentation 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

qq M qqq B

• 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!


Reco: Single Particle Observables

Reco: Single Particle Observables

consistent description of spectra, ratios and RAA


2

2

2 2

3

2 2

2 2

2

2

2

3

2

1 2

and

1 6

33

3

3

p t

p t

p pt t

p t

M

Bt

t

pv

pv

p p

v p

p

v

pv

v

v

Parton Number Scaling of v2

Parton Number Scaling of v2

smoking gun for recombination

measurement of partonic v2 !

•in leading order of v2, recombination predicts:

2 2

2 2

22

33

pM

p

t

B t

t

t

pv

p

v

p v

p

v

note that scaling breaks down in the fragmentation

domain


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


Two-Particle CorrelationsTwo-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 atintermediate pT

very similar to p+p; jet fragmentation?• analyze as function of integrated yield:

simple recombination of uncorrelated thermal quarks cannot reproduce two particle correlations

( )1

( ) ( )AB A B

ABA

dN d N NY

N d d

0.94

cone

0

AB ABY d Y


Recombination: Inclusion of Correlations

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:

21234 1 3 4 1 iji j

wW w Cw w

1234

6

3 3 A A BBA

BA

B

ABC d

dd

N

d P d PW


Thermal Recombination beyond the

Valence Quark Approximation

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:

1

10

1

20

1

30

1 ,

1 , ,

1 , , ,

a b a b a b a b

a b c a b c a b c a b c

a b c d a b c d a b c d a b c d

M dx dx x x c x x q x q x

dx dx dx x x x c x x x q x q x g x

dx dx dx dx x x x x c x x x x q x q x q x q x

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)20.5 GeV2 degrees of freedom likely dominated by lowest Fock state (i.e. valence quark state)


Higher Fock States: v2 Scaling Violations

Higher Fock States: v2 Scaling Violations

Generalization of scaling law to higher Fock states:• assume all partons carry roughly equal momentum

xi1/nν

with nν the number of partons in the Fock state

• valence quark approximation: ν=1, n1=2,3 and C1=1

(scaled v2 identical to parton v2)

general result:

( )2 2 /Hv P C n v P n

( )( ) ( ) ( )2 2

( )( ) ( ) ( )2 2

2 /2

3 /3

MM M M

BB B B

nv p C v p n

nv p C v p n

( ) ( )2 2 2M Bv p v p v p

scaling violations 5%

P. Sorensen, QM05


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


Last Words…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!!


The End


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: TC180 MeV

Rajagopal & Wilczek, hep-ph/0011333

Fodor & Katz, hep-lat/0110102




• technical progress: finer mesh size, physical quark masses, improved fermion actions

phase-transition: smooth, rapid cross-over critical temperature: TC193±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. bassprobing the qgp at rhic #1 steffen a. bass duke university probing the qgp at rhic:...

Documents

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mach cone angular correlation