Hot and Dense QCD Matter

and Heavy-Ion Collisions

Ralf Rapp

Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

MLL Colloquium TU München, 22.10.09

1.) Introduction: Pillars of the Strong Force

• Stable Matter: u , d , e- mu,d ≈ 5-10 MeV

But:

00 |h|G d,u

• quarks “glued” together ► Confinement

• proton mass Mp= 940 MeV >> 3mq ≈ 20 MeV

► Mass Generation (>95% visible mass)

u

d u

Quantum Chromo Dynamics:

• “strong” coupling for Q < 2GeV (r > 0.1fm)• QCD vacuum filled by condensates

2

41

aq Gq)m̂Agi(q QCDL

GeV.~|qq|G~*mq 35000 “constituent” quark mass

= g2/4

• hadrons overlap, quarks liberated Deconfinement (energy density ~ (# d.o.f )T4 , crit ≈ 1 GeV / fm3 )

/ T4 free gas

[Cheng et al ’08]

1.2 Quark-Gluon Plasma

Excite vacuum (hot+dense matter)

But:

• matter around Tc strongly coupled: “sQGP” ( – 3p ≠ 0 !)

-• ‹0|qq|0› condensate “melts”, mq* → 0

Mass Degeneration (hadron masses?)

‹qq›T / ‹qq›vac --

3p / T4

LatticeQCD ’08

|

|

1.3 QCD Phase Diagram and NatureEarly Universe(few s after Big Bang) Compact

Stellar Objects(Neutron Stars)

Unique opportunity to study:• primordial Big Bang matter • quark (de-) confinement and mass (de-) generation• matter with smallest known viscosity (/s): “near perfect fluid”• phase structure of non-abelian gauge theory (↔ string theory!?)

1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram

2.) Experimental Probes of QCD Matter

Particle Spectra in Heavy-Ion Collisions

3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!

4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra

5.) Conclusions

Outline

“Freeze-Out”Hadron Gas (≈ 10fm/c)

QGP ?! (≈ 5fm/c)

Au + Au

2.1 The “Little Bang” in the Laboratory

Au + Au → X

e+

e-

Questions:• Thermalization?• QGP Signatures??• QGP Properties???

c,b

2.2 Basic Findings at RHIC: Hadron Spectra

(1) Ideal Hydrodynamics: pT ≤ 2GeV [Shuryak, Heinz, …]

v2had

early thermalization, 0 ≤ 1fm/c

...])cos()p(v[dp

dNpd

dNT

TT

221 222

∂ T = 0 T= (+P) u u – P g

Input: equation of state (P), initial conditions, freezeout

Output: collective flow u

radial + elliptic (v2)

2 GeV ≤ pT ≤ 6 GeV(2) Quark Coalescence:

• baryon-to-meson “anomaly” • “quark-number scaling” of elliptic flow

)p(f)p(f|)q(|qd)(

pdg

pd

dNE qqqqMM

M 2333 2

[Greco et al ‘03 Fries et al ‘03, Hwa et al ’03]

hadronization via qq → M, qqq → B

(instantaneous, no spatial dependence of v2 in fq )

_

matter at RHIC thermalizes, 0 > c , small viscosity, partonic

ET - m =

Rati

o

2.3 Problems + Advanced Tools

• Key Questions:

- microscopic origin of “near perfect fluid”? How “perfect”? - matter constituents / spectral functions? …

• Heavy Quarks (charm, bottom): created early, Brownian particle traversing QGP fluid ► transport coefficients ↔ thermalization and “flow” ► Q-Q bound states (J/, Y) in QGP?

• Electromagnetic Emission (photons, dileptons): escape medium unaffected, “thermal radiation”

► dilepton invariant mass: (Mee )2 = (pe++pe )2

↔ direct access to in-medium spectral functions

-c,b

e+

e-

1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram

2.) Experimental Probes of QCD Matter

Particle Spectra in Heavy-Ion Collisions

3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!

4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra

5.) Conclusions

Outline

3.1 The Virtue of Heavy Quarks (Q=b,c)

• Large scale mQ >> QCD

→ “factorization” even at low pT

→ QQ produced in primordial N-N collisions

→ well “calibrated” initial spectra at all pT

• Large scale mQ >> T

→ thermal momentum pth2 = 3mQT >> T2 ~ Q2 therm. mom. transfer

→ Brownian motion (elastic scattering) → thermalization delayed by mQ/T memory of rescattering

• Flavor conserved in hadronization → coalescence!?

• Elastic scattering Q2 = q02 – q2 ~ (q2/2mQ)2 – q2 ~ -q2

→ quasi-static potential approach!? → common framework for heavy-quark diffusion and quarkonia

-

QmDT

2

2

p

fD

p)pf(

tf

• Brownian

Motion:

scattering rate diffusion coefficient

3.2 Heavy Quark Diffusion in the QGP

Fokker Planck Eq.[Svetitsky ’88,…]Q

q)p,q(wqdp 3 23

21 q)p,q(wqdD

• pQCD elastic scattering:

1= therm ≥ 20 fm/c slow

q,g

c

Microscopic Calculations of Diffusion

2

2elast

D

scg ~

[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore ‘04]

• D-/B-resonance model:

1= therm ~ 5 fm/c c

“D”

c

_q

_q

c)(

qG DDDcq 2

v1 L

parameters: mD , GD[van Hees+RR ’04]

3.2.2 Potential Scattering using Lattice QCD

• potential: use lattice QCD Q-Q internal energy (T>Tc):

TSUF QQQQ

• T-matrix for Q-q scatt. in QGP , GqQ: Q-q propagator

)E(T)E(GVdkkV)E(T LQqLLL 2

• HQ potential concept established in vacuum (EFT, lattice)

• 3-D reduced Bethe-Salpeter Eq.

QQQQQQ U)r(U)r(V

• Meson and diquark “resonances” for T ≤ 1.5 Tc

[Brambilla, Vairo et al]

3.3 Comparison of Drag Coefficients(Thermal Relaxation Rate)

• proliferation?! NB: pQCD ↔ Coulomb ↔ AdS/CFT T-matrix: Coulomb + ”string”(latQCD), resummed • “melting” resonances: relax = 1/ ~ 5-8 fm/c ~ constant

T [GeV]

[1

/fm

]

[Gubser ’06]

[Peshier ‘06; Gossiaux+Aichelin ’08]

[van Hees+RR ’04]

[van Hees,Mannarelli, Greco+RR ’07]

3.4 Heavy Flavor Phenomenology at RHIC

• Medium Evolution - hydrodynamics or parameterizations thereof

- realistic bulk-v2 (~5-6%)

- stop evolution after QGP; hadronic phase?

• Hadronization - fragmentation: c → D + X

- coalescence: c + q → D, adds momentum and v2

• Semileptonic Electron Decays - D, B → e± X , ~ conserve v2 and RAA of parent meson

- charm/bottom composition in p-p

[Hirano et al ’06]

→ relativistic Langevin simulations of heavy quark in QGP:

3.4.2 Model Predictions vs. RHIC Data

Semileptonic e± Spectra [PHENIX ’06]

• c-q → D coalescence increases both RAA and v2

• radiative E-loss upscaled pQCD • Langevin with resonances + coalescence• Langevin with upscaled pQCD elastic (Ds ~ 30/2T)

RAA≡ (dN/dpT )AA / (dN/dpT )pp

no coal.

3.4.3 T-Matrix Approach vs. e± Spectra at RHIC

• hadronic resonances at ~Tc ↔ quark coalescence

• connects 2 pillars of RHIC! (strong coupl. + coalescence)

[van Hees,Mannarelli,Greco+RR ’07]

Spatial Diffusion Ds = T/(mQ

3.5 Viscosity in sQGP?• Conjectured bound of sCFT (string-theo. methods):

• use heavy-quark diffusion to estimate for QGP: kinetic theory: s ≈n <p> tr /s = 1/5 T Ds

sCFT:s≈ Ds= 1/2 T Ds

close toTc

41

s[Kovtun,Son +Starinets ’05]

462 )(

s

[Lacey et al ’06]

[RR+van Hees ‘08]

3.6 “Reinterpretation” of Quark Coalescence “Resonance Recombination Model”: resonance scattering q+q → M close to Tc using Boltzmann eq.-

[Ravagli et al ’08]

~pd

dNM3

• conserves energy, recovers thermal equilibrium, encodes v2(x) in fq(x,p)

• Langevin, interaction strength determines v2max ≈7%

• approximate scaling in KT=ET -m

Quarks Mesons

2

1.) Introduction: QCD and QGP Quark Confinement + Hadron Mass Quark-Gluon Plasma + QCD Phase Diagram

2.) Experimental Probes of QCD Matter

Particle Spectra in Heavy-Ion Collisions

3.) Heavy-Quark Probes (c,b) Heavy-Quark Diffusion in the QGP Viscosity?!

4.) Electromagnetic Radiation The Visible Mass in the Universe?! Melting Vector Mesons + Dilepton Spectra

5.) Conclusions

Outline

4.) Electromagnetic Radiation

Tiqx )(j)x(jexdi)q(Π 0emem

4em

EM Correlation Function:

e+

e-)T,q(f

Mqdxd

dN Bee023

2

44 Im Πem(M,q;B,T)

Dilepton Sources: Relevance:

- Quark-Gluon Plasma: high mass + temp. qq → e+e , … M > 1.5GeV, T >Tc

- Hot + Dense Hadron Gas: M ≤ 1 GeV → e+e , … T ≤ Tc

-

q

q

_

e+

e

e+

e

Im Πem ~ Im D

>>

B*,a1,K1

...

N,,K…

4.2 -Meson in Medium: Hadronic Interactions

D(M,q;B ,T) = [M 2 - m2 - - B - M ] -1-Propagator:

[Chanfray et al, Herrmann et al, RR et al, Weise et al, Koch et al, Mosel et al, Eletsky et al, Oset et al, Lutz et al…]

= B,M=Selfenergies:

Constraints: decays: B,M→ N, scattering: N → N, A, …

B /0

0 0.1 0.7 2.6

[RR,Wambach et al ’99]

Meson “Melting” Switch off Baryons

4.3 Dilepton “Excess” Spectra at SPS

• “average” (T~150MeV) ~ 350-400 MeV

(T~Tc) ≈ 600 MeV → m

• fireball lifetime: FB ~ (6.5±1) fm/c[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]

)y,M(Acc),T;q,M(qxdd

dNq

qMd)(Vd

dMdN

iFB

fo

44

therm

0

3therm

0

Thermal Emission Spectrum:

4.3.2 NA60 Data vs. In-Medium Dimuon Rates

• acceptance-corrected data directly reflect thermal rates!

M[GeV] [RR,Wambach et al ’99]

[van Hees+RR ’07]

4.3.3 Low-Mass Dileptons at RHIC: PHENIX

• Successful approach at SPS fails at RHIC

5.) Conclusions

• Strong-Interaction (QCD) Matter

- Quark (de-) confinement, Mass (de-) generation

- Can be studied in heavy-ion collisions

- “Near perfect” liquid?!

• (Some) Recent Developments

- non-perturbative heavy-quark diffusion above Tc (“QGP liquid”)

- -resonance melts toward Tc (“hadron liquid”)

• Upcoming Experimental Programs:

- LHC (CERN), RHIC-2 (BNL), FAIR (GSI), NICA (Dubna), …

- “perturbative” QGP at high T?

- 1st order transition at finite B > 0?

3.2.3 AdS/CFT-QCD Correspondence

[Gubser ‘07]

pdtdp 2

2 SYMc

CFT/ADS Tm

cCFT/ADS m

T)..(2

5012

• match energy density (d.o.f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD

3-momentum independent

[Herzog et al, Gubser ‘06]

≈ (4-2 fm/c)-1 at T=180-250 MeV

Lat-QCD

TQCD ~ 250 MeV

But: “Higgs” Mechanism in Strong Interactions:qq attraction “Bose” condensate fills QCD vacuum

Spontaneous Chiral Symmetry Breaking

3.1 Chiral Symmetry + QCD Vacuum

)m( d,u 0QCD L : isospin + “chiral” (left/right-handed) invariant

350000 fm|qqqq||qq| LRRL

>

>

>

>qLqR

qL-qR

--

Profound Consequences:• effective quark-mass: ↔ mass generation

• massless Goldstone bosons 0,± , pion pole-strength f= 93MeV

• “chiral partners” split, M ≈ 0.5GeV:

00 |qq|m*q

JP=0± 1± 1/2±

• Weinberg Sum Rule(s)

3.1.2 Hadron Spectra + Chiral Symm. Breaking

Axial-/Vector Correlators

)Im(Ims

dsf IA

IV

112

pQCD cont.

“Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85]

● chiral breaking: |q2| ≤ 1 GeV2

Constituent Quark Mass

3.2.2 Dilepton Rates: Hadronic vs. QGP

dRee /dM2 ~ ∫d3q f B(q0;T) Im em

• Hard-Thermal-Loop [Braaten et al ’90]

enhanced over Born rate

• Hadronic and QGP rates “degenerate” around ~Tc

• Quark-Hadron Duality at all M ?! ( degenerate axialvector SF!)

[qq→ee] [HTL]

-

• Relativistic Langevin simulations for heavy quarks in QGP fireball

4.2 Heavy-Quark Spectra in Au-Au at RHIC

[van Hees,Greco+RR ’05]

Nuclear Modification Factor

• factor 3-4 stronger effects due to resonance interactions• bottom quarks little affected

Elliptic FlowRAA≡ (spec)AA /(spec)pp

4.4 Heavy-Light Quark T-Matrix in QGP

)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T Qq02

• lattice-QCD based quark “potentials” FQQ =UQQ –T SQQ

• meson + diquark “resonances” up to ~1.5 Tc

[van Hees et al ‘08]

3.2 EM Spectral Function in VacuumR = (e+e → hadrons) / (e+e→) ~ Im em(M)

Imem ~ [Im D+ Im D/10 + Im D/5]

M ≤ 1 GeV: non-perturbative (vector-meson resonance)

M > 1.5 GeV: perturbative (qq continuum)

Im em ~ Nc ∑(eq)2

C)T(fMqxdd

dN Bee23

2

44Low-mass

dilepton rate:-mesondominated! Im D

√s=M-

e+

e-

e+

e-

q

q

-

R

3.4Meson in Cold Nuclear Matter

+ A → e+e X e+

e

Nuclear Photo-Production:

invariantmass

spectra

[Riek et al ’08]Theoretical Approach:

Mee[GeV]

Fe - Ti

N ≈ 0.5 0

N

elementary production amplitude

in-medium spectral function+

[CLAS/JLab ‘08]

well tested at high energies, Q2 > 1 GeV2:

• perturbation theory (s = g2/4π << 1)

• degrees of freedom = quarks + gluons

1.2 Quantum Chromodynamics (QCD)

2

41

aq Gq)m̂Agi(q QCDL

(mu ≈ md ≈ 5-10MeV )

[Nobel approved, 2004]

Q2 ≤ 1 GeV2 → transition to “strong” QCD:

• effective d.o.f. = hadrons (Confinement)• massive “constituent” quarks, mq* ≈ 350 MeV ≈ ⅓ Mp (Chiral Symmetry Breaking)

↕ ⅔ fm

4.7 Q-Q Bound States in the QGP: J/

J/ + g c + c + X←→ -

Suppression +Regeneration:

-

J/D

D -

J/c- c reaction equilibrium rate limit

Nuclear Modification Factors

Centrality Dependence Momentum Dependence

[Zhao+RR ’08, ‘09]

)NN(d

dN eq

4.1 Heavy-Quarks and Single-e± Spectra• Radiative energy-loss of heavy quarks?• Thermalization and collective flow? • Consistency?• experimental tool: electron spectra D,B → eX

c,b

pT [GeV/c]

RA

A =

(A

A)

/ (p

p)

Djordjevic etal. ‘04

Armesto etal.‘05

Elliptic Flow Nuclear Modification Factor

• radiative transport coefficient larger than theory (~ 3-5)q̂

[Armesto et al ’05]

?

• origin of strong interactions?• bottom “contamination”?

• 3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG

Stot = exp[-nuc L] exp[-QGP QGP ] exp[-HGHG ]

• Regeneration in QGP + HG: microscopically: backward reaction (detailed balance!)

key ingredients: reaction rate equilibrium limit ( -width) )m,m,N( *

ccc (links to lattice QCD)

)NN(d

dN eq

4.) Heavy Quarkonia in Medium4.1 Basic Elements and Connections to URHICs

[PBM etal ’01, Gorenstein etal ’02,Thews etal ’01, Ko etal ’02, Grandchamp+RR ’02, Cassing etal ‘03] J/ + g c + c + X←→ -

for thermal c-quarks and gluons:

5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS

Expanding Fireball + pQCD

• pQCD+Cronin at qt >1.6GeV T0=205MeV suff., HG dom.

• addt’l meson-Bremsstrahlung → K→K substantial at low qt

[Liu+ RR’05]

WA98 “Low-qt Anomaly”

[Turbide,RR+Gale’04]

• thermal radiation qt<3GeV ?!

• QGP window 1.5<qt<3GeV ?!

5.1.2 Thermal Photons II: RHIC

• also: -radiation off jets• shrinks QGP window qt<2GeV ?!

[Gale,Fries,Turbide,Srivastava ’04]

3.3.5 Charmonium Width+Mass from Lattice QCD

[Umeda+ Matsufuru ’05]using constrained curve fitting (Breit-Wigner functions)

c and J/ Width

• ”jumps” across Tc

• qualitatively consistent with partonic dissociation

c and J/ Mass

• essentially constant

3.5 Dilepton Spectra in Heavy-Ion Collisions (SPS)→ Evolve dilepton rates over thermal fireball expansion

• show in-medium broadening• normalized• “distorted” by exp. acceptance

+ Mass Spectra [NA60, 2005]

drop. mass (norm.)

M[GeV]

• quantitative agreement • exhibits Boltzmann slope (T)• invariant-mass spectrum!

Acc.-corrected+ Spectra [NA60, 2009]

M[GeV]

[van Hees+RR ’08]