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Life Above the Hagedorn Temperature Quark-Gluon Plasma at SPS, RHIC & LHC

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Life Above the Hagedorn Temperature Quark-Gluon Plasma at SPS, RHIC & LHC Life Above the Hagedorn Temperature Quark-Gluon Plasma at SPS, RHIC & LHC Berndt Mueller Brookhaven National Laboratory & Duke University Hagedorn Symposium CERN 13 November 2015 1965 was a momentous year cosmic microwave background Hagedorn mass spectrum 2 2015 almost unimaginable progress RHIC 3He+Au Planck: cosmological parameters PHENIX: QGP in p/d/3He+Au 3 Three things are needed… …to reach the summit: good equipment, good strategy, determination. In the study of hot, dense QCD matter this means: • High luminosity colliders • Large acceptance, high DAQ rate detectors with good particle ID • Realistic lattice QCD for thermo- dynamic quantities • Realistic transport codes • Weak (pQCD) and strong (AdS/CFT) coupling dynamical models • Multivariate model-data comparison After several decades of experimental and theoretical development, the necessary tools are now all in place. 4 The Relativistic Heavy Ion Collider …is hexagonal and 3.8 km long RHIC-AGS Complex at BNL 5 The Relativistic Heavy Ion Collider …is hexagonal and 3.8 km long RHIC-AGS Complex at BNL 5 The highest energies… 6 The highest energies… CMS ATLAS 6 Equation of State of QCD Matter 7 Equation of State EOS of flowing matter has conservative and dissipative contributions: (cons) (diss) Tµν = Tµν + Tµν = (ε + p)uµuν − pgµν 2 α α +η(∂µ uν + ∂ν uµ − 3 gµν ∂α u ) +ζ gµν ∂α u α When ζ(∂αu ) > p, the matter becomes unstable and cavitates. In general, Tµν is a dynamical quantity that relaxes to its equilibrium value on a time scale τπ that itself is related to the viscosity. While the shear viscosity η has a lower quantum bound, the bulk viscosity ζ vanishes for conformally invariant matter. 8 QCD EOS at μB = 0 Results (true quark masses, continuum extrapolated) have converged; full agreement found between groups (HotQCD, Wuppertal-Budapest) using different quark actions. 9 (Pseudo-) Critical temperature Transition between hadron gas and quark-gluon plasma is a cross-over at µB = 0 and for small µB. Precise value of Tc depends on the quantity used to define it. Pseudo-critical temperature from chiral susceptibility peak: Tc = 154 ± 9 MeV Uncertainty in Tc, not width of cross-over region! 10 Hadron mass spectrum Below Tc, the quantity (ε−3p)/T4 measures the Hagedorn spectrum (TH ≈ 180 MeV): level density of massive hadronic excitations Aem/TH of the QCD vacuum. ρ m = H ( ) 2 2 5/4 (m + m0 ) Lines: Hadron resonance gas using only PDG resonances Data points: Lattice QCD LQCD lies above HRG for T > 140 MeV Indicates additional hadron resonances 11 Hadron mass spectrum Below Tc, the quantity (ε−3p)/T4 measures the Hagedorn spectrum (TH ≈ 180 MeV): level density of massive hadronic excitations Aem/TH of the QCD vacuum. ρ m = H ( ) 2 2 5/4 (m + m0 ) Lines: Hadron resonance gas using only PDG resonances In good agreement with lattice results Data points: Lattice QCD Hadrons up to 3 GeV mass contribute LQCD lies above HRG for T > 140 MeV 4 Indicates additional hadron resonances Ê Ê mcut = 3.0 GeV 3 Ê mcut = 2.5 GeV 4 Ê T ê L Ê mcut = 2.0 GeV P 2 3 - e Ê H mcut = 1.7 GeV 1 Ê Ê Ê 0 100 110 120 130 140 150 160 170 T MeV 11 H L Probing the baryon spectrum Consistency of µs/µB and µB/T with chemical composition of emitted hadrons and Lattice QCD requires additional strange baryon resonances beyond those in the PDG tables. Quark model states of strange baryons 12 QCD EOS at μB ≠ 0 Borszanyi et al., arXiv:1204:6710 Approximate trajectories in QCD phase diagram 13 Probing the QCD Phase Boundary 14 QCD Phase Diagram Lattice QCD LHC equation of state RHIC Borsanyi et al. Quark-Gluon Critical end point ? 154±9 MeV Tc Plasma RHIC BES Hadronic Matter Color Super- conductor Nuclei Neutron µB stars 15 Thermodynamic fluctuations Susceptibilities measure thermodynamic fluctuations. Interesting because they exhibit singularities at a critical point. Fluctuations of conserved quantities (charge Q, baryon number B,…) cannot be changed by local final-state processes. Lattice gauge theory: Ratios are independent of the (unknown) freeze-out volume: 16 Chemical freeze-out … from fluctuations of conserved quantum numbers (Q, B): Compare lattice results with the STAR data for the fluctuation ratios in the temperature range 140−150 MeV permits to read off µB. Both methods are consistent with each other and with the measured baryon/antibaryon ratios, if additional strange baryon states beyond those in the PDG tables (e.g. in the quark model) are accounted for. 17 Chemical freeze-out hadron abundances fluctuations Consistency of freeze-out parameters from mean hadron abundances and from fluctuations (Q, B) opens the door to search for a critical point in the QCD phase diagram by looking for enhanced critical fluctuations as function of beam energy. 18 Probing the Quark-Gluon Plasma 19 Hot QCD matter properties Which properties of hot QCD matter can we hope to determine and how ? 20 Hot QCD matter properties Which properties of hot QCD matter can we hope to determine and how ? Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 20 Hot QCD matter properties Which properties of hot QCD matter can we hope to determine and how ? Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation 4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭ 20 Hot QCD matter properties Which properties of hot QCD matter can we hope to determine and how ? Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation 4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭ Hard Πµν (k) = d 4 x eikx j µ (x) jν (0) QGP Radiance: Lepton pairs, photons for em ∫ LQCD 20 Hot QCD matter properties Which properties of hot QCD matter can we hope to determine and how ? Easy T ⇔ ε, p,s Equation of state: spectra, coll. flow, fluctuations for µν LQCD 1 4 η = d x Txy (x)Txy (0) Shear viscosity: anisotropic collective flow T ∫ 4π 2α C ⎫ Very qˆ = s R dy− U †F a+i (y− )UF a+ (0) N 2 −1 ∫ i ⎪ Hard c ⎪ for 4π 2α C ⎪ eˆ = s R dy− iU † ∂− Aa+ (y− )UAa+ (0) Momentum/energy diffusion: LQCD 2 ∫ ⎬ Nc −1 ⎪ parton energy loss, jet fragmentation 4πα s † a0i a b0i b ⎪ κ = ∫ dτ U F (τ )t UF (0)t ⎪ 3Nc ⎭ Hard Πµν (k) = d 4 x eikx j µ (x) jν (0) QGP Radiance: Lepton pairs, photons for em ∫ LQCD Easy 1 † a a mD = − lim ln U E (x)UE (0) Color screening: Quarkonium states for |x|→∞ | x | LQCD 20 The “perfect” fluid 21 Viscous hydrodynamics Hydrodynamics = effective theory of energy and momentum conservation energy-momentum tensor = ideal fluid + dissipation µν µν µ ν µν µν ∂µT = 0 with T = (ε + P)u u − Pg + Π µν λ ⎡ dΠ µ νλ ν µλ du ⎤ µ ν ν µ µν τ ⎢ + u Π + u Π ⎥ = η ∂ u + ∂ u − trace − Π Π dτ ( ) dτ ( ) ⎣ ⎦ Input: Equation of state P(ε), shear viscosity, initial conditions ε(x,0), uμ(x,0) Shear viscosity η is normalized by density: kinematic viscosity η/ρ. Relativistically, the appropriate normalization factor is the entropy density s = (ε+P)/T, because the particle density is not conserved: η/s. 22 Elliptic flow • two nuclei collide rarely head-on, but mostly with an offset: Reaction z plane only matter in the overlap area gets compressed and heated y x dN ⎛ ⎞ 2π = N0 ⎜1+ 2∑vn (pT ,η)cosn(φ −ψ n (pT ,η))⎟ dφ ⎝ n ⎠ anisotropic flow coefficients event plane angle 23 Event-by-event fluctuations Initial state generated in A+A collision is grainy event plane ≠ reaction plane WMAP ⇒ eccentricities ε1, ε2, ε3, ε4, etc. ≠ 0 Idea: Energy density fluctuations in transverse plane from initial state quantum fluctuations. These thermalize to different temperatures locally and then propagate hydrodynamically to generate angular flow velocity fluctuations in the final state. ⇒ flows v1, v2, v3, v4,... 24 Elliptic flow “measures” ηQGP Universal strong coupling limit of Schenke, Jeon, Gale, PRL 106 (2011) 042301 non-abelian gauge theories with a gravity dual: /s=0 η/s → 1/4π v η/s = 0 2 /s=0.08 /s=0.16 η/s = 1/4π aka: the “perfect” liquid 0.2 η/s = 2/4π 0.15 0.1 Au+Au 200 GeV 0.05 30-40% central STAR data 0 0 0.5 1 1.5 2 2.5 pT [GeV] Schenke, Jeon, Gale, PRC 85 (2012) 024901 25 RHIC vs. LHC Saturated Glasma Gale, Jeon, Schenke, Tribedy, Venugopalan, arXiv:1209.6330 LHC MC-Glauber 0.7 0.6 BM & A. Schäfer, PRD 85 (2012) 114030 0.5 RHIC e ê 0.4 De 0.3 0.2 0.1 0.0 0.2 0.4 0.6 0.8 z fm 26 H L Shape engineering: U+U collisions STAR Constituent-quark Glauber model and IP-Glasma model are consistent with the observations, but not the nucleon-nucleon based Glauber model.
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