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,

1.) Introduction: Pillars of the Strong Force Stable Matter: u, d, e - m u,d ≈ 5-10 MeV But: quarks “glued” together ► Confinement proton mass M p = 940 MeV >> 3m q ≈ 20 MeV ► Mass Generation (>95% visible mass) u d u  Quantum Chromo Dynamics: “strong” coupling for Q 0.1fm) QCD vacuum filled by condensates “constituent” quark mass = g 2 /4 

hadrons overlap, quarks liberated  Deconfinement (energy density  ~ (# d.o.f )T 4,  crit ≈ 1 GeV / fm 3 )  / T4 / T4 free gas [Cheng et al ’08] 1.2 Quark-Gluon Plasma Excite vacuum (hot+dense matter) But: matter around T c strongly coupled: “sQGP” (  – 3p ≠ 0 !) - ‹0|qq|0› condensate “melts”, m q * → 0  Mass Degeneration (hadron masses?) ‹qq› T / ‹qq› vac - - 3p / T 4 Lattice QCD ’08

| | 1.3 QCD Phase Diagram and Nature Early 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

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: p T ≤ 2GeV [Shuryak, Heinz, …] v 2 had  early thermalization,  0 ≤ 1fm/c ∂  T  = 0 T  = (  +P) u  u – P g  Input: equation of state  (P), initial conditions, freezeout Output: collective flow u  radial + elliptic (v 2 )

2 GeV ≤ p T ≤ 6 GeV (2) Quark Coalescence: baryon-to-meson “anomaly” “quark-number scaling” of elliptic flow [Greco et al ‘03 Fries et al ‘03, Hwa et al ’03]  hadronization via qq → M, qqq → B (instantaneous, no spatial dependence of v 2 in f q ) _  matter at RHIC thermalizes,  0 >  c, small viscosity, partonic E T - m = Ratio

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: (M ee ) 2 = (p e+ +p e  ) 2 ↔ direct access to in-medium spectral functions - c,b e+ e-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 m Q >>  QCD → “factorization” even at low p T → QQ produced in primordial N-N collisions → well “calibrated” initial spectra at all p T Large scale m Q >> T → thermal momentum p th 2 = 3m Q T >> T 2 ~ Q 2 therm. mom. transfer → Brownian motion (elastic scattering) → thermalization delayed by m Q /T  memory of rescattering Flavor conserved in hadronization → coalescence!? Elastic scattering Q 2 = q 0 2 – q 2 ~ (q 2 /2m Q ) 2 – q 2 ~ -q 2 → quasi-static potential approach!? → common framework for heavy-quark diffusion and quarkonia -

Brownian Motion: scattering rate diffusion coefficient 3.2 Heavy Quark Diffusion in the QGP Fokker Planck Eq. [Svetitsky ’88,…] Q pQCD elastic scattering:    1  =  therm ≥ 20 fm/c slow q,g c Microscopic Calculations of Diffusion [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 parameters: m D, G D [van Hees+RR ’04]

3.2.2 Potential Scattering using Lattice QCD potential: use lattice QCD Q-Q internal energy (T>T c ):  T-matrix for Q-q scatt. in QGP, G qQ : Q-q propagator HQ potential concept established in vacuum (EFT, lattice) 3-D reduced Bethe-Salpeter Eq. Meson and diquark “resonances” for T ≤ 1.5 T c [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-v 2 (~5-6%) - stop evolution after QGP; hadronic phase? Hadronization - fragmentation: c → D + X - coalescence: c + q → D, adds momentum and v 2 Semileptonic Electron Decays - D, B → e ± X, ~ conserve v 2 and R AA 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 R AA and v 2 radiative E-loss upscaled pQCD Langevin with resonances + coalescence Langevin with upscaled pQCD elastic (D s ~ 30/2  T) R AA ≡ (dN/dp T ) AA / (dN/dp T ) pp

no coal T-Matrix Approach vs. e ± Spectra at RHIC hadronic resonances at ~T c ↔ quark coalescence connects 2 pillars of RHIC! (strong coupl. + coalescence) [van Hees,Mannarelli,Greco+RR ’07] Spatial Diffusion D s = T/(m Q 

3.5 Viscosity in sQGP? Conjectured bound of sCFT (string-theo. methods): use heavy-quark diffusion to estimate for QGP: kinetic theory:  s ≈  n tr /s = 1/5 T D s sCFT:  s  ≈  D s    = 1/2 T D s close to  T c  [Kovtun,Son +Starinets ’05] [Lacey et al ’06] [RR+van Hees ‘08]

3.6 “Reinterpretation” of Quark Coalescence “Resonance Recombination Model”: resonance scattering q+q → M close to T c using Boltzmann eq. - [Ravagli et al ’08]  conserves energy, recovers thermal equilibrium, encodes v 2 (x) in f q (x,p) Langevin, interaction strength determines v 2 max ≈ 7% approximate scaling in K T =E T -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 EM Correlation Function: e+ e-e+ e- Im Π em (M,q;  B,T) Dilepton Sources: Relevance: - Quark-Gluon Plasma: high mass + temp. qq → e + e , … M > 1.5GeV, T >T c - Hot + Dense Hadron Gas: M ≤ 1 GeV       → e + e , … T ≤ T c - qqqq _ e+ee+e  e+ee+e   Im Π em ~ Im D 

> >    B *,a 1,K 1... N, ,K … 4.2  -Meson in Medium: Hadronic Interactions D  (M,q;  B,T) = [M 2 - m  2 -   -   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 /  [RR,Wambach et al ’99]  Meson “Melting” Switch off Baryons

4.3 Dilepton “Excess” Spectra  at SPS “average”   (T~150MeV) ~ MeV    (T~T c ) ≈ 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] 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 T c (“QGP liquid”) -  -resonance melts toward T c (“hadron liquid”) Upcoming Experimental Programs: - LHC (CERN), RHIC-2 (BNL), FAIR (GSI), NICA (Dubna), … - “perturbative” QGP at high T? - 1 st order transition at finite  B > 0?

3.2.3 AdS/CFT-QCD Correspondence [Gubser ‘07] 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= MeV Lat-QCD T QCD ~ 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 : isospin + “chiral” (left/right-handed) invariant > > > > qLqL qRqR qLqL - qRqR - - Profound Consequences: effective quark-mass: ↔ mass generation massless Goldstone bosons  0,±, pion pole-strength f  = 93MeV “chiral partners” split,  M ≈ 0.5GeV: J P =0 ± 1 ± 1/2 ±

Weinberg Sum Rule(s) Hadron Spectra + Chiral Symm. Breaking Axial-/Vector Correlators pQCD cont. “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] ● chiral breaking: |q 2 | ≤ 1 GeV 2 Constituent Quark Mass

3.2.2 Dilepton Rates: Hadronic vs. QGP dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em Hard-Thermal-Loop [Braaten et al ’90] enhanced over Born rate Hadronic and QGP rates “degenerate” around ~T c 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 Flow R AA ≡ (spec) AA /(spec) pp

4.4 Heavy-Light Quark T-Matrix in QGP lattice-QCD based quark “potentials” F QQ =U QQ –T S QQ meson + diquark “resonances” up to ~1.5 T c [van Hees et al ‘08]

3.2 EM Spectral Function in Vacuum R =  (e + e  → hadrons) /  (e + e  →     ) ~ Im  em (M) Im  em ~ [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 ~  N c ∑(e q ) 2 Low-mass dilepton rate:   -meson dominated!  Im D  √s=M - e+e-e+e-  e+e-e+e- qqqq - R

3.4  Meson in Cold Nuclear Matter  + A → e + e  X  e+ ee+ e  Nuclear Photo-Production: invariant mass spectra [Riek et al ’08] Theoretical Approach: M ee  [GeV] Fe - Ti  N ≈ 0.5  0  N  elementary production amplitude in-medium  spectral function + [CLAS/JLab ‘08]

well tested at high energies, Q 2 > 1 GeV 2 : perturbation theory (  s = g 2 /4π << 1) degrees of freedom = quarks + gluons 1.2 Quantum Chromodynamics (QCD) (m u ≈ m d ≈ 5-10MeV ) [Nobel approved, 2004] Q 2 ≤ 1 GeV 2 → transition to “strong” QCD: effective d.o.f. = hadrons (Confinement) massive “constituent” quarks, m q * ≈ 350 MeV ≈ ⅓ M p (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 - c - c reaction equilibrium rate limit Nuclear Modification Factors Centrality Dependence Momentum Dependence [Zhao+RR ’08, ‘09]

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 p T [GeV/c] R AA = (AA) / (pp) Djordjevic etal. ‘04 Armesto etal.‘05 Elliptic Flow Nuclear Modification Factor radiative transport coefficient larger than theory (~ 3-5) [Armesto et al ’05] ? origin of strong interactions? bottom “contamination” ?

3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG S tot = exp[-  nuc   L] exp[-  QGP  QGP ] exp[-  HG   HG ] Regeneration in QGP + HG: microscopically: backward reaction (detailed balance!) key ingredients: reaction rate equilibrium limit (  -width) (links to lattice QCD) 4.) Heavy Quarkonia in Medium 4.1 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 Thermal Photons I : SPS Expanding Fireball + pQCD pQCD+Cronin at q t >1.6GeV  T 0 =205MeV suff., HG dom. addt’l meson-Bremsstrahlung  →   K→  K  substantial at low q t [Liu+ RR’05] WA98 “Low-q t Anomaly” [Turbide,RR+Gale’04]

thermal radiation q t <3GeV ?! QGP window 1.5<q t <3GeV ?! Thermal Photons II: RHIC also:   -radiation off jets shrinks QGP window q t <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 T c 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]