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Hot and Dense QCD Matter and Heavy-Ion Collisions

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 M ünchen , 22.10.09. = g 2 /4 p.  Quantum Chromo Dynamics: “ strong” coupling for Q < 2GeV ( r > 0.1fm )

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Hot and Dense QCD Matter and Heavy-Ion Collisions

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  1. 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

  2. = g2/4p •  Quantum Chromo Dynamics: • “strong” coupling for Q < 2GeV (r > 0.1fm) • QCD vacuum filled by condensates “constituent” quark mass 1.) Introduction:Pillars of the Strong Force u • Stable Matter:u , d , e- • mu,d ≈ 5-10 MeV • But: u d • quarks “glued” together►Confinement • proton massMp= 940 MeV >> 3mq ≈ 20 MeV • ► Mass Generation(>95% visible mass)

  3. - • ‹0|qq|0›condensate “melts”,mq* → 0 •  Mass Degeneration • (hadron masses?) - - ‹qq›T /‹qq›vac 1.2 Quark-Gluon Plasma Excite vacuum (hot+dense matter) free gas e/T4 • hadrons overlap, quarks liberated •  Deconfinement • (energy density e~ (# d.o.f )T4, • ecrit ≈ 1GeV/fm3 ) 3p/T4 Lattice QCD ’08 [Cheng et al ’08] • But: • matter around Tc strongly coupled: • “sQGP” (e – 3p ≠ 0 !)

  4. | | 1.3 QCD Phase Diagram and Nature Early Universe (few ms 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 (h/s): “near perfect fluid” • phase structure of non-abelian gauge theory (↔ string theory!?)

  5. Outline 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

  6. 2.1 The “Little Bang” in the Laboratory e+ e- c,b r Au + Au QGP ?! (t ≈ 5fm/c) Hadron Gas (t ≈ 10fm/c) “Freeze-Out” • Questions: • Thermalization? • QGP Signatures?? • QGP Properties??? Au + Au → X

  7. v2had  early thermalization, t0 ≤ 1fm/c 2.2 Basic Findings at RHIC:Hadron Spectra (1) Ideal Hydrodynamics:pT ≤ 2GeV [Shuryak, Heinz, …] ∂m Tmn = 0 Tmn = (e+P) um un – P gmn Input: equation of state e(P), initial conditions, freezeout Output: collective flow um radial + elliptic (v2)

  8. (2) Quark Coalescence: 2GeV ≤ pT ≤ 6GeV Ratio ET - m = • baryon-to-meson “anomaly” • “quark-number scaling” of elliptic flow _ hadronization via qq → M, qqq → B [Greco et al ‘03 Fries et al ‘03, Hwa et al ’03] (instantaneous, no spatial dependence of v2 in fq )  matter at RHIC thermalizes, e0 > ec, small viscosity, partonic

  9. 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-Qbound states (J/y, 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- r

  10. Outline 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

  11. 3.1 The Virtue of Heavy Quarks (Q=b,c) • Large scale mQ >> LQCD • → “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 ~ Q2therm. 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 -

  12. _ _ q q “D” c c 3.2 Heavy Quark Diffusion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion coefficient Microscopic Calculations of Diffusion q,g c • pQCD elastic scattering:g-1= ttherm ≥ 20 fm/cslow [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore ‘04] • D-/B-resonance model:g-1= ttherm ~ 5 fm/c parameters: mD , GD [van Hees+RR ’04]

  13. 3.2.2 Potential Scattering using Lattice QCD • HQ potential concept established • in vacuum (EFT, lattice) • 3-D reduced Bethe-Salpeter Eq. [Brambilla, Vairo et al] • T-matrix for Q-q scatt. in QGP , GqQ: Q-q propagator • potential: use lattice QCD • Q-Qinternal energy (T>Tc): _ • Meson and diquark “resonances” • for T ≤ 1.5 Tc

  14. 3.3 Comparison of Drag Coefficients(Thermal Relaxation Rate) [Gubser ’06] [Peshier ‘06; Gossiaux+Aichelin ’08] g [1/fm] [van Hees+RR ’04] [van Hees,Mannarelli, Greco+RR ’07] T [GeV] • proliferation?! NB: pQCD ↔ Coulomb ↔ AdS/CFT • T-matrix: Coulomb + ”string”(latQCD), resummed • “melting” resonances: trelax = 1/g ~ 5-8 fm/c ~ constant

  15. 3.4 Heavy Flavor Phenomenology at RHIC → relativistic Langevin simulations of heavy quark in QGP: • 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±n X , ~ conserve v2 and RAA of parent meson • - charm/bottom composition in p-p [Hirano et al ’06]

  16. 3.4.2 Model Predictions vs. RHIC Data Semileptonic e±Spectra [PHENIX ’06] RAA≡ (dN/dpT )AA / (dN/dpT )pp • radiative E-loss upscaled pQCD • Langevin with resonances • + coalescence • Langevin with upscaled • pQCD elastic (Ds ~ 30/2pT) • c-q → Dcoalescence • increases bothRAA and v2

  17. Spatial Diffusion Ds = T/(mQg) 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) no coal. [van Hees,Mannarelli,Greco+RR ’07]

  18. [Lacey et al ’06] [RR+van Hees ‘08] 3.5 Viscosity in sQGP? [Kovtun,Son +Starinets ’05] • Conjectured bound of sCFT (string-theo. methods): • use heavy-quark diffusion to estimate for QGP: kinetic theory: h/s ≈ 4/15 n <p> ltr /s = 1/5 T Ds  sCFT: h/s≈ 1/4p Ds(2pT) = 1/2 T Ds close toTc

  19. 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 3.6 “Reinterpretation” of Quark Coalescence “Resonance Recombination Model”: resonance scattering q+q → M close to Tc using Boltzmann eq. [Ravagli et al ’08] - 

  20. Outline 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

  21. e+ e- q q _ Dilepton Sources:Relevance: - Quark-Gluon Plasma: high mass + temp. qq → e+e-, …M>1.5GeV, T>Tc - Hot + Dense Hadron Gas: M≤ 1GeV p+p- → e+e-, … T ≤ Tc - e+ e- p- p+ r(770) 4.) Electromagnetic Radiation EM Correlation Function: e+ e- g* Im Πem(M,q;mB,T) Im Πem ~ Im Dr

  22. 4.2 r-Meson in Medium: Hadronic Interactions > rB /r0 0 0.1 0.7 2.6 > rMeson “Melting” Switch off Baryons [RR,Wambach et al ’99] [Chanfray etal, Herrmann etal, RR etal, Weise etal, Koch etal, Mosel etal, Eletsky et al, Oset etal, Lutz etal…] Dr (M,q;mB ,T) = [M 2 - mr2 -Srpp -SrB -SrM ] -1 r-Propagator: B*,a1,K1... r Sp r SrB,rM= Selfenergies: Srpp= N,p,K… Sp Constraints: decays: B,M→ rN, rp, ... ; scattering:pN→rN, gA, …

  23. 4.3 Dilepton “Excess” Spectra at SPS Thermal Emission Spectrum: • “average” Gr (T~150MeV) ~ 350-400 MeV • Gr (T~Tc) ≈ 600 MeV → mr • fireball lifetime: tFB ~ (6.5±1) fm/c [van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]

  24. 4.3.2 NA60 Data vs. In-Medium Dimuon Rates Mmm [GeV] [van Hees +RR ’07] [RR,Wambach et al ’99] • acceptance-corrected data directly reflect thermal rates!

  25. 4.3.3 Low-Mass Dileptons at RHIC: PHENIX • Successful approach at SPS fails at RHIC

  26. 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”) • - r-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 mB > 0?

  27. 3.2.3 AdS/CFT-QCD Correspondence 3-momentum independent [Herzog et al, Gubser ‘06] • match energy density • (d.o.f = 120 vs. ~40) • and coupling constant • (heavy-quark potential) • to QCD Lat-QCD TQCD ~ 250 MeV  ≈ (4-2 fm/c)-1 at T=180-250 MeV [Gubser ‘07]

  28. qR qL • Profound Consequences: • effective quark-mass: • ↔ mass generation • massless Goldstone bosonsp0,±, • pion pole-strength fp = 93MeV • “chiral partners” split,DM ≈ 0.5GeV: > > > > - - qL qR JP=0±1± 1/2± 3.1 Chiral Symmetry + QCD Vacuum : isospin + “chiral” (left/right-handed) invariant But: “Higgs” Mechanism in Strong Interactions: qq attraction “Bose” condensate fills QCD vacuum Spontaneous Chiral Symmetry Breaking -

  29. 3.1.2 Hadron Spectra + Chiral Symm. Breaking Axial-/Vector Correlators Constituent Quark Mass “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] pQCD cont. • Weinberg Sum Rule(s) ● chiral breaking:|q2| ≤ 1 GeV2

  30. - [qq→ee] [HTL] 3.2.2 Dilepton Rates: Hadronic vs. QGPdRee /dM2 ~ ∫d3q f B(q0;T) ImPem • 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!)

  31. 4.2 Heavy-Quark Spectra in Au-Au at RHIC • Relativistic Langevin simulations for heavy quarks in QGP fireball Nuclear Modification Factor Elliptic Flow RAA≡ (spec)AA /(spec)pp • factor 3-4 stronger effects due to resonance interactions • bottom quarks little affected [van Hees,Greco+RR ’05]

  32. meson + diquark “resonances” • up to ~1.5 Tc [van Hees et al ‘08] 4.4 Heavy-Light Quark T-Matrix in QGP • lattice-QCD based quark “potentials” • FQQ =UQQ –T SQQ

  33. Low-mass dilepton rate: r-meson dominated! ImDr  3.2 EM Spectral Function in Vacuum R = s(e+e- → hadrons) / s(e+e-→m+m-) ~ Im Pem(M) R - e+ e- q q e+ e- r √s=M M ≤ 1 GeV: non-perturbative (vector-meson resonance) M > 1.5 GeV: perturbative (qq continuum) - ImPem~ [ImDr + ImDw /10 + ImDf /5] ImPem ~ Nc∑(eq)2

  34. 3.4 r Meson in Cold Nuclear Matter Theoretical Approach: [Riek et al ’08] Fe-Ti in-medium r spectral function elementary production amplitude + rN ≈ 0.5 r0 r g N Mee[GeV] Nuclear Photo-Production: e+ e- r g invariant mass spectra g + A → e+e- X [CLAS/JLab ‘08]

  35. Q2≤ 1GeV2 → transition to “strong” QCD: • effective d.o.f. = hadrons (Confinement) • massive “constituent” quarks, • mq* ≈ 350 MeV ≈ ⅓ Mp (Chiral Symmetry • Breaking) ↕⅔fm 1.2 Quantum Chromodynamics (QCD) [Nobel approved, 2004] • well tested at high energies, Q2>1GeV2: • perturbation theory (as = g2/4π<< 1) • degrees of freedom = quarks + gluons (mu ≈ md ≈ 5-10MeV )

  36. - D - D J/y reaction equilibrium rate limit - c c J/y Nuclear Modification Factors Centrality Dependence Momentum Dependence 4.7 Q-Q Bound States in the QGP: J/y Suppression + Regeneration: - → ← J/y + g c + c + X [Zhao+RR ’08, ‘09]

  37. 4.1 Heavy-Quarks and Single-e± Spectra RAA = (AA) / (pp) Djordjevic etal. ‘04 Armesto etal.‘05 pT [GeV/c] • Radiative energy-loss of heavy quarks? • Thermalization and collective flow? • Consistency? • experimental tool: electron spectra D,B → eX c,b Nuclear Modification Factor Elliptic Flow ? [Armesto et al ’05] • radiative transport coefficient • larger than theory (~ 3-5) • origin of strong interactions? • bottom “contamination”?

  38. - → ← J/y + g c + c + X key ingredients: reaction rate equilibrium limit (y -width) (links to lattice QCD) 4.) Heavy Quarkonia in Medium4.1 Basic Elements and Connections to URHICs • 3-Stage Dissociation:nuclear (pre-eq) -- QGP -- HG • Stot = exp[-snucrL] exp[-GQGPtQGP ] exp[-GHGtHG ] • Regeneration in QGP + HG: • microscopically: backward reaction (detailed balance!) [PBM etal ’01, Gorenstein etal ’02,Thews etal ’01, Ko etal ’02, Grandchamp+RR ’02, Cassing etal ‘03] for thermal c-quarks and gluons:

  39. WA98 “Low-qt Anomaly” • addt’l meson-Bremsstrahlung • pp→ ppgpK→pKg • substantial at low qt [Liu+ RR’05] 5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS Expanding Fireball + pQCD • pQCD+Cronin at qt >1.6GeV •  T0=205MeV suff., HG dom. [Turbide,RR+Gale’04]

  40. 5.1.2 Thermal Photons II: RHIC • thermal radiation qt<3GeV ?! • QGP window 1.5<qt<3GeV ?! • also: g-radiation off jets • shrinks QGP window qt<2GeV ?! [Gale,Fries,Turbide,Srivastava ’04]

  41. 3.3.5 Charmonium Width+Mass from Lattice QCD [Umeda+ Matsufuru ’05] using constrained curve fitting (Breit-Wigner functions) hcand J/y Mass hcand J/y Width • ”jumps” across Tc • qualitatively consistent with • partonic dissociation • essentially constant

  42. 3.5 Dilepton Spectra in Heavy-Ion Collisions (SPS) Acc.-corrected m+m-Spectra [NA60, 2009] Mmm [GeV] • quantitative agreement • exhibits Boltzmann slope (T) • invariant-mass spectrum! [van Hees+RR ’08] → Evolve dilepton rates over thermal fireball expansion m+m-Mass Spectra [NA60, 2005] drop. mass (norm.) Mmm [GeV] • show in-medium r broadening • normalized • “distorted” by exp. acceptance

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