1. Steffen A. BassBulk QCD Matter: from RHIC to LHC #1 Steffen A. Bass Duke University RHIC: the emerging picture Modeling of Relativistic Heavy-Ion Collisions Relativistic Fluid Dynamics Hybrid Macro+Micro Transport Model Validation: RHIC Predictions for LHC Spectra & Yields Collective Flow Transport Coefficients: Low Viscosity Matter at LHC? Dynamics of hot & dense QCD matter: from RHIC to LHC collaborators: J. Ruppert T. Renk C. Nonaka B. Mueller A. Majumder M. Asakawa

2. Steffen A. BassBulk QCD Matter: from RHIC to LHC #2 RHIC: the emerging picture

3. Steffen A. BassBulk QCD Matter: from RHIC to LHC #3 Exploring QCD Matter at RHIC and LHC initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Lattice-Gauge Theory: rigorous calculation of QCD quantities works in the infinite size / equilibrium limit Experiments: observe the final state + penetrating probes rely on QGP signatures predicted by Theory Phenomenology & Transport Theory: connect QGP state to observables provide link between LGT and data

4. Steffen A. BassBulk QCD Matter: from RHIC to LHC #4 Current Picture of QGP Structure: - Lessons from RHIC - Jet-Qenching & Elliptic Flow: QGP produced at RHIC has very large opacity behaves like an ideal fluid (vanishing viscosity) Lattice Gauge Theory & Parton Recombination: at T C, QGP degrees of freedom carry the quantum numbers of quarks and recombine to form hadrons Applicability of Ideal Fluid Dynamics and Statistical Model: matter produced is thermalized thermalization (isotropization) occurs very early, ~0.6 fm/c

5. Steffen A. BassBulk QCD Matter: from RHIC to LHC #5 Modeling of Relativistic Heavy-Ion Collisions

6. Steffen A. BassBulk QCD Matter: from RHIC to LHC #6 Survey of Transport Approaches

7. Steffen A. BassBulk QCD Matter: from RHIC to LHC #7 Relativistic Fluid Dynamics

8. Steffen A. BassBulk QCD Matter: from RHIC to LHC #8 Relativistic Fluid Dynamics transport of macroscopic degrees of freedom based on conservation laws:  μ T μν =0  μ j μ =0 for ideal fluid: T μν = ( ε +p) u μ u ν - p g μν and j i μ = ρ i u μ Equation of State needed to close system of PDE’s: p=p(T, ρ i )  connection to Lattice QCD calculation of EoS initial conditions (i.e. thermalized QGP) required for calculation assumes local thermal equilibrium, vanishing mean free path  applicability of hydro is a strong signature for a thermalized system

9. Steffen A. BassBulk QCD Matter: from RHIC to LHC #9 3D-Hydro: Validation at RHIC separate chemical f.o. simulated by rescaling p,K 1 st attempt to address all data w/ 1 calculation b=6.3 fm Nonaka & Bass: PRC75, 014902 (2007) See also Hirano; Kodama et al.

10. Steffen A. BassBulk QCD Matter: from RHIC to LHC #10 Ideal RFD: Challenges centrality systematics of v 2 less than perfect no flavor dependence of cross-sections separation chemical and kinetic freeze-out: normalize spectra by hand PCE: proper normalization, wrong v 2 Nu Xu Viscosity: success of ideal RFD argues for a low viscosity in QGP phase  compatible with AdS/CFT bound of 1/4π viscosity will stongly change as function of temperature during collision  need to account for viscous corrections in hadronic phase Csernai HG: Prakash et al. QGP: Arnold, Moore & Yaffe

11. Steffen A. BassBulk QCD Matter: from RHIC to LHC #11 Hybrid Hydro+Micro Approaches

12. Steffen A. BassBulk QCD Matter: from RHIC to LHC #12 Full 3-d Hydrodynamics QGP evolution Cooper-Frye formula UrQMD t fm/c hadronic rescattering Monte Carlo Hadronization TCTC T SW Bass & Dumitru, PRC61,064909(2000) Teaney et al, nucl-th/0110037 Nonaka & Bass, PRC75, 014902 (2007) Hirano et al. nucl-th/0511046 3D-Hydro + UrQMD Model ideally suited for dense systems –model early QGP reaction stage well defined Equation of State parameters: –initial conditions –Equation of State Hydrodynamics + micro. transport (UrQMD) no equilibrium assumptions  model break-up stage  calculate freeze-out  includes viscosity in hadronic phase parameters: –(total/partial) cross sections matching condition: use same set of hadronic states for EoS as in UrQMD generate hadrons in each cell using local T and μ B

13. Steffen A. BassBulk QCD Matter: from RHIC to LHC #13 3D-Hydro+UrQMD: Validation  good description of cross section dependent features & non- equilibrium features of hadronic phase  hydrodynamic evolution used for calculation of hard probes

14. Steffen A. BassBulk QCD Matter: from RHIC to LHC #14 Predictions for LHC

15. Steffen A. BassBulk QCD Matter: from RHIC to LHC #15 Initial Conditions @ LHC  required for all hydro-based calculations can be obtained from:  ab-inito calculations of initial state  analysis of LHC data  phenomenological extrapolation of RHIC data PHOBOS extrapolation: extend longitudinal scaling self-similar trapezoidal shape Saturation model scaling: ASW: dN ch /d  =1650 KLN: dN ch /d  =1800-2100 EHNRR: dN ch /d  =2570 U. Wiedemann QM06

16. Steffen A. BassBulk QCD Matter: from RHIC to LHC #16 3D-Hydro+UrQMD: Initial Conditions Initial Conditions: –energy density –baryon number density –parameters: –flow profile: Equation of State –1st order phase transition –T c =160 MeV switching temperature –T SW =150 MeV v T =0 v L =  Bjorken’s solution);  0,  max, n Bmax,  0,   RHICLHC-BjLHC-1LHC-2  0 (fm) 0.60.30.2  0 (GeV/fm 3 ) 552301000500 00 0.5N/A1.0  1.4N/A6.0 transverse plane note that LHC-Bj initial conditions were not meant to provide a reasonable guess for LHC but rather elucidate a scenario more extreme than RHIC longitudinal profile

17. Steffen A. BassBulk QCD Matter: from RHIC to LHC #17 Spectra & Yields Disclaimer: do not take the following “predictions” too seriously they only represent placeholders to demonstrate the capabilities of this particular transport approach once data are available, the parameters of the initial condition will be adjusted in order to establish whether 3D-Hydro+UrQMD can provide a viable description of QGP dynamics at LHC

18. Steffen A. BassBulk QCD Matter: from RHIC to LHC #18 Blast from the Past: Bj-Hydro+UrQMD SAB & A. Dumitru: Phys. Rev. C61 064909 (2000): boost-invariant 1+1D RFD with UrQMD as hadronic afterburner RFD validated with SPS data [Dumitru & Rischke: PRC59 354 (1999)]  dynamic transition from QGP & mixed phase to hadronic phase increase in as function of hadron mass less than linear due to flavor- dependence of hadronic rescattering

19. Steffen A. BassBulk QCD Matter: from RHIC to LHC #19 From SPS to LHC from RHIC to LHC: lifetime of QGP phase nearly doubles only 33% increase in collision numbers of hadronic phase

20. Steffen A. BassBulk QCD Matter: from RHIC to LHC #20 3D-Hydro+UrQMD: Multiplicities dN/dy at y CM LHC-1LHC-2 ++ 1715904 K+K+ 228123 p5734 0+00+0 3319 ++ 4.32.5 -- 0.850.52

21. Steffen A. BassBulk QCD Matter: from RHIC to LHC #21 3D-Hydro+UrQMD: Spectra

22. Steffen A. BassBulk QCD Matter: from RHIC to LHC #22 3D-Hydro+UrQMD: dissipative effects significant dissipative effects  early chemical freeze-out manifest in proton distribution (pure Hydro would need PCE) hadronic phase “cools” pion spectrum built-up of radial flow for heavier particles  pion wind

23. Steffen A. BassBulk QCD Matter: from RHIC to LHC #23 Hybrid RFD+Boltzmann Summary validated at RHIC for soft sector and jet energy-loss treatment of viscosity in hadronic phase separation of thermal & chemical freeze-out  allows for consistent treatment of bulk matter dynamics and hard probes

24. Steffen A. BassBulk QCD Matter: from RHIC to LHC #24 Collective Flow

25. Steffen A. BassBulk QCD Matter: from RHIC to LHC #25 Collision Geometry: Elliptic Flow elliptic flow (v 2 ): gradients of almond-shape surface will lead to preferential emission in the reaction plane asymmetry out- vs. in-plane emission is quantified by 2 nd Fourier coefficient of angular distribution: v 2  calculable with fluid-dynamics Reaction plane x z y  The applicability of fluid-dynamics suggests that the medium is in local thermal equilibrium!  Note that fluid-dynamics cannot make any statements how the medium reached the equilibrium stage…

26. Steffen A. BassBulk QCD Matter: from RHIC to LHC #26 spatial eccentricity momentum anisotropy initial energy density distribution: Elliptic flow: early creation time evolution of the energy density: P. Kolb, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909 Most hydro calculations suggest that flow anisotropies are generated at the earliest stages of the expansion, on a timescale of ~ 5 fm/c if a QGP EoS is assumed.

27. Steffen A. BassBulk QCD Matter: from RHIC to LHC #27 3D-Hydro (+UrQMD): Elliptic Flow dissipative effects in hadronic phase do not affect built-up of elliptic flow  robust early time signal no significant sensitivity to the two initial conditions ( note Kolb, Sollfrank & Heinz: PLB459 (1999) 667: only small rise)

28. Steffen A. BassBulk QCD Matter: from RHIC to LHC #28 Transport Coefficients: Low Viscosity Matter M. Asakawa, S.A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301 Prog. Theo. Phys. 116 (2006) 725

29. Steffen A. BassBulk QCD Matter: from RHIC to LHC #29 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Viscosity: from RHIC to LHC expanding hadron gas w/ significant & increasing mean free path: large viscosity large elliptic flow & success of ideal RFD: zero/small viscosity viscosity of matter changes strongly with time & phase Hydro+UrQMD: viscous corrections for hadron gas phase how to understand low viscosity in QGP phase? will low viscosity features persist at LHC?

30. Steffen A. BassBulk QCD Matter: from RHIC to LHC #30 The sQGP Dilemma microscopic transport theory shows that assuming quasi-particle q & g degrees of freedom would require unphysically large parton cross sections to match elliptic flow data even for λ  0.1 fm (close to uncertainty bound) dissipative effects are large  does a small viscosity have to imply that matter is strongly interacting?  consider effects of (turbulent) color fields  the success of ideal hydrodynamics has led the community to equate low viscosity with a vanishing mean free path and thus large parton cross sections: strongly interacting QGP (sQGP) D. Molnar

31. Steffen A. BassBulk QCD Matter: from RHIC to LHC #31 Anomalous Viscosity Plasma physics: –A.V. = large viscosity induced in nearly collisionless plasmas by long-range fields generated by plasma instabilities. Astrophysics - dynamics of accretion disks: –A.V. = large viscosity induced in weakly magnetized, ionized stellar accretion disks by orbital instabilities. Biophysics: –A.V. = The viscous behavior of nonhomogenous fluids, e.g., blood, in which the apparent viscosity increases as flow or shear rate decreases toward zero. Can the QGP viscosity be anomalous? –Expanding plasmas (e.g. QGP @ RHIC) have anisotropic momentum distributions –plasma turbulence arises naturally in plasmas with an anisotropic momentum distribution (Weibel-type instabilities).  soft color fields generate anomalous transport coefficients, which may give the medium the character of a nearly perfect fluid even at moderately weak coupling. Anomalous Viscosity:  any contribution to the shear viscosity not explicitly resulting from momentum transport via a transport cross section

32. Steffen A. BassBulk QCD Matter: from RHIC to LHC #32 Weibel (two-stream) instability Ultra-Relativistic Heavy-Ion Collision: two streams of colliding color charges consider the effect of a seed magnetic field with induced current creates B, adds to seed B opposing currents repel each other: filamentation  exponential Weibel instability Guy Moore, McGill Univ. pos. charges deflect as shown: alternately focus and defocus neg. charges defocus where pos. focus and vice versa  net-current induced, grows with time

33. Steffen A. BassBulk QCD Matter: from RHIC to LHC #33 Hard Thermal Loops: Instabilities find HTL modes for anisotropic distribution:  for any ξ  0 there exist unstable modes  energy-density and growth rate of unstable modes can be calculated: Romatschke & Strickland, PRD 68: 036004 (2003) Arnold, Lenaghan & Moore, JHEP 0308, 002 (2003) Mrowczynski, PLB 314, 118 (1993) Nonabelian Vlasov equations describe interaction of “hard” (i.e. particle) and “soft” color field modes and generate the “hard-thermal loop” effective theory: Effective HTL theory permits systematic study of instabilities of “soft” color fields:

34. Steffen A. BassBulk QCD Matter: from RHIC to LHC #34 Anomalous Viscosity Derivation: Sketch linear Response: connect η with momentum anisotropy Δ : use color Vlasov-Boltzmann Eqn. to solve for f and Δ : Turbulent color field assumption: ensemble average over fields:  diffusive Vlasov-Boltzmann Eqn: example: anomalous viscosity in case of transverse magnetic fields complete calculation of η via variational principle:

35. Steffen A. BassBulk QCD Matter: from RHIC to LHC #35 collisional viscosity: derived in HTL weak coupling limit anomalous viscosity: induced by turbulent color fields, due to momentum-space anisotropy with ansatz for fields:  for reasonable values of g:  A <  C Collisional vs. Anomalous Viscosity M. Asakawa, S.A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301 Prog. Theo. Phys. 116 (2006) 725

36. Steffen A. BassBulk QCD Matter: from RHIC to LHC #36 Time-Evolution of Viscosity initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out viscosity: ? relaxation rates are additive  sumrule for viscosities:  smaller viscosity dominates in system w/ 2 viscosities! temperature evolution:

37. Steffen A. BassBulk QCD Matter: from RHIC to LHC #37 Viscosity at LHC: Two Scenarios field picture: (turbulent) color fields induce an anomalous viscosity, which keeps the total shear-viscosity small during the QGP evolution  perfect liquidity in the weak coupling limit collisional picture: weaker coupling at LHC vs. RHIC will lead to a larger viscosity  increase in dissipative effects, deviations from ideal fluid  elliptic flow at LHC compared to RHIC can act as a decisive measurement for the dominance of anomalous viscosity

38. Steffen A. BassBulk QCD Matter: from RHIC to LHC #38 Summary and Outlook Heavy-Ion collisions at RHIC have produced a state of matter which behaves similar to an ideal fluid  Hydro+Micro transport approaches are the best tool to describe the soft, non-perturbative physics at RHIC after QGP formation  at LHC, such hybrid models should perform well if QGP matter is found to have a low viscosity a small viscosity does not necessarily imply strongly interacting matter!  (turbulent) color fields induce an anomalous viscosity, which keeps the total sheer-viscosity small during the QGP evolution  elliptic flow at LHC as decisive measurement on impact of anomalous viscosity Note: due to it’s slow & nearly isotropic expansion, the early Universe most likely did not have an anomalous contribution to its viscosity

39. Steffen A. BassBulk QCD Matter: from RHIC to LHC #39 The End

40. Steffen A. BassBulk QCD Matter: from RHIC to LHC #40 Elliptic Flow: ultra-cold Fermi-Gas Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra- relativistic heavy-ion collisions  Elliptic flow is a general feature of strongly interacting systems!