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The Quark-Gluon Plasma Four Lectures

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The Quark-Gluon Plasma Four Lectures The Quark-Gluon Plasma Four Lectures Helmut Satz Universit¨at Bielefeld, Germany LN Frascati March 2011 The Fundamental Problems of Physics constituents forces quarks strong leptons e-m gluons, photons weak vector bosons (Z, W ±) gravitation Higgs unification, TOE elementary interactions ⇓ complex systems states of matter transitions solid, liquid, gas thermal phase transitions glass, gelatine percolation transitions insulator, conductor scaling and renormalization superconductor, ferromagnet critical exponents fluid, superfluid universality classes Complex Systems ⇒ New Direction in Physics • Given constituents and dynamics of elementary systems, what is the behaviour of complex systems? • What are the possible states of matter and how can they be specified? • How do transitions from one state of matter to another occur? • Is there a general pattern of critical phenomena, independent of specific dynamics? • Conceptually new physics: renormalization, self-similarity, self- organization, emergence, sand piles, swarm intelligence, ... Knowing all there is to know about the helium atom the ant tells you nothing about the behaviour of liquidhelium acolonyofants ⇒ even a fully unified fundamental theory does not solve the issue of complex systems, of the states of matter Fire hot dry Void Air Earth Aether wet cold Water states of matter in antiquity - and in strong interaction physics? Four Lectures 1. The Thermodynamics of Quarks and Gluons 2. Phase Diagram of Strongly Interacting Matter 3. Quarkonia in Deconfined Matter 4. Statistical Hadronization and its Origin Lecture 1 The Thermodynamics of Quarks and Gluons What is the Quark-Gluon Plasma? A state of strongly interacting matter, in which the constituents of hadrons, quarks and gluons, are not spatially confined to form color-neutral bound states. Nucleon Gas Nuclear Matter Quark Matter When many hadrons overlap, quarks cannot identify “their hadron”, the concepts of a hadron and of confinement become meaningless, color screening and high quark density (asymptotic freedom) forbid hadronic scales ⇒ transition to a new state of matter Confined Matter • quark-antiquark pairs or three-quark states form color-neutral states of hadronic size ∼ 1 fm; • quarks acquire a dynamically generated “effective” mass of about 300 MeV by gluon dressing → spontaneous chiral symmetry breaking; • mesonic matter: constituents are mesons and baryons, the inter- action is resonance-dominanted; • baryonic matter: constituents are nucleons, the interaction is long-range attraction (1 fm) and short range repulsion (0.5 fm) increasing the meson density (by increasing T ), or increasing the nucleon density (by compressing nuclear matter) leads to hadron overlap and thus deconfinement. what happens in the deconfinement transition? Deconfined Matter • at deconfinement, bound states are dissolved, constituents are colored quarks; ⇒ insulator-conductor transition of QCD • the gluon dressing melts, the quark mass drops to Lagrangian mass; ⇒ chiral symmetry restoration. do the two phenomena coincide? In general: either yes or first deconfinement, then chiral symmetry restoration [Banks & Casher 1979] • possible state of deconfined massive colored quarks: quark plasma; lattice studies: at low baryon density, deconfinement and chiral symmetry restoration coincide; • deconfined quarks (whether massive or not) may still interact; QCD ⇒ quark-quark binding ⇒ colored bosonic diquarks; • colored diquark bosons at low T can form Bose condensate: color superconductor. Speculative phase diagram for strongly interacting matter: T quark−gluon plasma Tc mesonic matter quark plasma nuclear matter color superconductor µ µ c NB: in all phases, ∃ interactions! 2. From Hadrons to Quarks and Gluons 2 π 4 1 4 simplest confined matter: ideal pion gas Pπ = 3 T ≃ T 90 3 simplest deconfined matter: ideal quark-gluon plasma 2 π 7 4 4 PQGP = { 2 × 8+ [2 × 2 × 2 × 3] } T − B ≃ 4 T − B 90 8 with bag pressure B for outside/inside vacuum given Pπ(T ) vs. PQGP (T ): nature chooses highest P (lowest F ) P QGP π 4 4 Tc T −B phase transition from hadronic matter at low T to QGP at high T critical temperature: 4 Pπ = PQGP → Tc ≃ 0.3 B ≃ 150 MeV with B1/4 ≃ 200 MeV from quarkonium spectroscopy corresponding energy densities 4 4 ǫπ ≃ T → ǫQGP ≃ 12 T + B ε T 4 QGP latent heat of deconfinement π 4 4 Tc T at Tc, energy density changes abruptly by latent heat of deconfinement compare energy density and pressure: ε T 4 4 ideal gas ǫ = 3P 3 P/ T here we obtain 4 4 Tc T and the interaction measure ∆(T) ǫ − 3P 4B ∆ ≡ = T 4 T 4 shows that for Tc ≤ T < 2 − 3 Tc the QGP is strongly interacting Tc T so far, simplistic model; real world? 3. Finite Temperature Lattice QCD given QCD as dynamics input, calculate resulting thermodynamics, based on QCD partition function ⇒ lattice regularization, computer simulation • energy density 16.0 14.0 ε /T4 ⇒ latent heat of deconfinement ε/T4 SB 12.0 For N = 2, 2+1: 10.0 f 8.0 6.0 3 flavour 2+1 flavour Tc ≃ 175 MeV 4.0 2 flavour 3 2.0 ǫ(T ) ≃ 0.5 − 1.0 GeV/fm T/Tc c 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 explicit relation to deconfinement, chiral symmetry restoration? ⇒ order parameters • deconfinement ⇒ mq → ∞ Polyakov loop L(T ) ∼ exp{−FQQ¯/T } ¯ FQQ¯: free energy of QQ pair for r → ∞ = 0 T <TL confinement L(T ) =6 0 T >TL deconfinement variation defines deconfinement temperature TL • chiral symmetry restoration ⇒ mq → 0 chiral condensate χ(T ) ≡ hψψ¯ i ∼ Mq measures dynamically generated (‘constituent’) quark mass =6 0 T <Tχ chiral symmetry broken χ(T ) = 0 T >Tχ chiral symmetry restored variation defines chiral symmetry temperature Tχ • how are TL and Tχ related? SU(N) gauge theory: ∼ spontaneous ZN breaking at TL QCD, chiral limit: ∼ explicit ZN breaking by χ(T ) → 0 at Tχ chiral symmetry restoration ⇒ deconfinement lattice results Polyakov loop & chiral condensate vs. temperature at µ = 0, ∃ one transition hadronic matter → QGP for Nf = 2,mq → 0 at Tc = TL = Tχ ≃ 175 MeV Finite temperature lattice QCD shows: – ∃ transition at T ∼ 0.175 ± ? GeV, where deconfinement & chiral symmetry restoration coincide – at transition, ǫ increases suddenly by latent heat of deconfinement What about interactions in QGP? interaction measure(trace of energy-momentum tensor) ǫ − 3P ∆ = T 4 vanishes for non-interacting massless constituents quarks and gluons are (ideally) massless; what ∆(T >Tc)? 0.4 9.0 (ε-3p)/T4 SU(3) 8.0 nf=3 n =2+1 SU(4) 7.0 f 0.3 SU(6) nf=2 6.0 nf=0 5.0 0.2 4.0 3.0 Delta/(N^2-1) 0.1 2.0 T/Tc 1.0 0 1 1.5 2 2.5 3 3.5 4 0.0 T/Tc 1.0 1.5 2.0 2.5 3.0 3.5 Datta & Gupta 2009 Karsch, Laermann & Peikert 2000 4. The Strongly Interacting QGP Expect that for high enough T , asymptotic freedom → ideal QGP (perturbation theory) how high is enough? – consider best known case SU(3) gauge theory ∃ perturbative calculations up to O(g5) 1.5 perturbation theory oscillates strongly 1.0 does not converge for T ≤ 10 Tc SB 2 p/p up to g 3 non-pert. extension [Kajantie et al. 2003]: up to g 0.5 4 up to g still qualitatively wrong for T ≤ 5 Tc 5 up to g 4d lattice 0.0 1 10 100 1000 T / Tc 2 ∆ 5 (T/Tc ) (T) re-organize perturbation theory 4 Lattice Data (“re-summed” theory, HTL) 3 [Andersen, Strickland & Su 2010] 2 NNLO 1 NLO LO 1 2 3 4T/Tc 5 – weak coupling approaches cannot account for QGP at T ≤ Tc ≤ 5 Tc: no dip at Tc, wrong (log) T -dependence Non-perturbative approach: bag model non-interacting quarks & gluons in “medium” gluon condensate 2 4B G0 ∆ = = 5 T 4 T 4 SU(3) - lattice (B/T^4)*(T/Tc)^2, B=0.012 Gev^4 4 (B/T^4)*(T/Tc)^2 - B=0.018 Gev^4 bag pressure ∼ gluon condensate at T = 0 3 2 4 2 numerical estimate G0 ≃ 0.012 GeV [Shifman,Vainshtein & Zakharov 1979] Delta*(T/Tc)^2 1 0 0 1 2 3 4 5 Conclude: T/Tc • weak coupling: T -dependence too weak, no dip at Tc • bag model: T -dependence too strong, no dip at Tc what is QGP for Tc ≤ T ≤ 4 Tc? ⇒ Quasi-Particle Model ∃ two regions • critical region as T → Tc, “singular” behavior • screening region in hot QGP consider gluons in deconfined medium: polarization → dressing, effective gluon mass – as T → Tc from above, correlation length increases/diverges, so gluon polarizes more & more of medium – as T >Tc increases, correlation length decreases, so gluon sees less and less of medium – as T >Tc increases, energy density of medium increases two competing effects: consider SU(2) gauge theory [Goloviznin & HS 1993] ⇒ continuous transition, critical exponents for T → Tc, with t ≡ (T/Tc), – energy density ǫ ∼ (t − 1)1−α −2ν−η – correlation volume Vcor ∼ (t − 1) with (Z2 universality class) α = 0.11, ν = 0.69, η = 0.04, so that 1−α−2ν−η −0.41 mcrit(T ) ∼ ǫ Vcor ∼ (t − 1) ∼ (t − 1) effective gluon mass diverges for T → Tc in hot QGP, screening length rD ∼ 1/T , hence – ǫ ∼ T 4 −3 m(t) – Vcor ∼ T a(t−1)−0.4 bt – mcrit(T ) ∼ ǫ Vcor ∼ T overall behavior of effective gluon mass −c m(T ) = a(t − 1) + bt t with constants a,b,c; here c = 0.41 1 2 3 retain this form in general 2.0 apply to SU(3) gauge theory 1.5 [Castorina, Miller & HS 2010] 1.0 2.0 3.0 4.0 excellent description of all thermodynamic quantities, including ∆(T ) NB: speed of sound in QGP “vanishes” at Tc, heavy gluons..
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