Heavy ion collisions at the LHC – theory C. Greiner Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik From SPS to RHIC to LHC Tomographic and diagnostic tools Recent theoretical developments: parton cascade, dissipative hydro, classical YM fields Summary

AGS : Si and Au ; up to  s =5 GeV /nucl pair only hadronic variables RHIC : 2000 Au ; up to  s = 200 GeV /nucl pair hadrons, photons, dileptons, jets SPS : S and Pb ; up to  s =20 GeV/nucl pair hadrons, photons and dileptons LHC : starting 2008 Pb ; up to  s = 5.5 TeV/nucl pair ALICE and CMS experiments

Exploring the phases of nuclear matter

RHIC’s Two Major Discoveries Discovery of strong “elliptic” flow: –Elliptic flow in Au + Au collisions at √s NN = 130 GeV, STAR Collaboration –1 citations Discovery of “jet quenching” –Suppression of hadrons with large momentum in central Au+Au collisions at √s NN = 130 GeV, PHENIX Collaboration –384 citations

Initial production of partons minijets string matter

LHC multiplicities LO pQCD GRV 94, no shadowing p 0 = 2 GeV Eskola, Kajantie, Z. Phys. C75 (1995) Pb+Pb → g N. Hammon et al, PRC 61 (2000) same as lower left plus EKS shadowing 3100 N. Borghini, U.A.Wiedemann, e-Print: arXiv: [hep-ph]

Saturation approaches Kharzeev et al, arXiv: Drescher, Nara, arXiv: Adil, Gyulassy, arXiv: charged particles ! (x 3/2 for total mult.) Lesson: dN ch /dy ~ 2000: Q s ≥ 2 GeV

Momentum space anisotropy Time dependence Michael Strickland

Electromagnetic signals from an anisotropic plasma Use evolving anisotropic momentum space distribution: instant isotropization (hydro) free streaming use interpolating model between these limits: Dilepton yield can be a measure for the isotropization of the plasma Martinez, Strickland, arXiv: Similar for photons: Schenke, Strickland, Phys.Rev.D76:025023,2007.

Colored-Particle-In-Cell (CPIC-) simulation Solve using smeared colored particles convergent results with less test particles Numerically solve the Vlasov equation coupled to the Yang Mills equation using a test particle ansatz, leading to the Wong-Yang-Mills equations: Investigate systems (early phase of HIC) that are locally anisotropic in momentum space: A. Dumitru, Y. Nara, M. Strickland Phys.Rev.D75:025016, 2007

Chromo-Weibel-instabilities In an anisotropic system Weibel instabilities occur due to current filamentation: Exponential growth of unstable field modes faster isotropization of hard particles Outlook: inclusion of hard collisions / particle-field conversion / jet physics A. Dumitru, Y. Nara, M. Strickland, Phys.Rev.D75:025016, 2007 B. Schenke, M. Strickland, C. Greiner, M.H. Thoma, Phys.Rev.D73:125004,2006

SU(2) visualization Michael Strickland Time Space

Motion Is Hydrodynamic x y z When does thermalization occur? –Strong evidence that final state bulk behavior reflects the initial state geometry Because the initial azimuthal asymmetry persists in the final state dn/d  ~ v 2 (p T ) cos (2  ) v 2

Relativistic Quantum Transport for URHIC microscopic transport calculations of partonic degrees of freedom RHIC, LHC new development Z. Xu and C. Greiner, PRC 71, (2005) Boltzmann Approach of MultiParton Scatterings (BAMPS) 3x3x collision probability particle in cell method

central elliptic flow in noncentral Au+Au collisions at RHIC: fast isotropization and thermalisation hydrodynamical evolution of momentum spectrum, … micr. determination of transport parameter … Z. Xu and C. Greiner, hep-ph/ Z. Xu and C. Greiner, NPA 774, 787 (2006)

Elliptic flow and shear viscosity parton cascade BAMPS (Z. Xu) viscous hydro P. Romatschke,nucl-th/

Thermalization time and entropy production Hydrodynamics: Israel-Stewart 2 nd order formalism for relativistic viscous hydro: stress viscosityshear (geom.)relax. time Entropy production bound constrains τ 0 and η /s Dumitru, Molnar, Nara, arXiv:

Dissipative Hydrodynamics Shear, bulk viscosity and heat conductivity of dense QCD matter could be prime candidates for the next Particle Data Group, if they can be extracted from data. Need a causal hydrodynamical theory. What are the criteria of applicability? Causal stable hydrodynamics can be derrived from the Boltzmann Equation: -Renormalization Group Method by Kunihiro/Tsumura-->stable 1 st Order linearized BE with f=f 0 +εf 1 +ε²f 2 yields (2nd Order – work in progress) can be solved by introducing projector P on Ker{A}, where A-linearized collision operator -Grad‘s 14-momentum method-->2 nd Order causal hydrodynamics. Calculate momenta of the BE. Transport coefficients and relaxation times for dissipative quantities can be calculated as functions of collision terms in BE. Compare dissipative relaxation times to the mean free pass from cascade simulation. Andrej El

Use strongly coupled N = 4 SUSY YM theory. Derive a quantum lower viscosity bound:  s > 1/4  AdS 5 /CFT Correspondence for Strongly- Coupled Systems Analogy between black hole physics and equilibrium thermodynamics Solutions called black branes Black branes possess hydrodynamic characteristics Similar to fluids – viscosity, diffusion constants,…. horizon Extra dimension (the bulk) MULTIPLICITY Entropy  Black Hole Area DISSIPATION Viscosity  Graviton Absorption

Au+Au: Systematic Suppression Pattern –  constancy for pT > 4 GeV/c for all centralities? Suppressed Enhanced

Jet quenching at the LHC GLV: Phys.Rev.Lett.89 Salgado, Wiedemann: Nucl.Phys.A747 Dainese, Loizides: Eur.Phys.J.C38 BDMPS GLV CERN-LHCC

Energy loss within BAMPS  full transport model  consistent inclusion of inelastic gg  ggg processes  effective LPM cut-off future investigation of:  RAA   angular correlations  energy redistribution ... (Boltzmann Approach to Multi-Particle Scattering) O. Fochler

Stronger longitudinal broadening caused by domains of strong chromo-fields with Explaining the “ridge” Additional near-side long range correlation in  (“ridge like” corrl.) observed. Dan Magestro, Hard Probes 2004, STAR, nucl-ex/ , Phys. Rev. C73 (2006) and P. Jacobs, nucl-ex/ Au+Au 0-10% STAR preliminary J. Putschke, QM2006 Dumitru, Nara, Schenke, Strickland e-Print: arXiv: [hep-ph]

Jet propagation Poynting vectors Dynamical simulation of jet propagation in the plasma Björn Schenke preliminary

Fluid Effects on Jets ? Mach cone? Jets travel faster than the speed of sound in the medium. – While depositing energy via gluon radiation. –QCD “sonic boom” –To be expected in a dense fluid which is strongly-coupled

High p T Parton  Low p T “Mach Cone” The “disappearance ” is that of the high pT partner But at low pT, see re- appearance and “Side-lobes” (Mach cones)

Barbara Betz, Dirk Rischke, Horst Stöcker, Giorgio Torrieri Mach Cones in Ideal Hydrodynamics Box Simulation Bjorken Expansion

AdS/CFT vs. pQCD tested by heavy quark energy loss Horowitz, Gyulassy: arxiv: AdS/CFT  drag coefficient on heavy quarks in a strongly-coupled SYM plasma heavy quark suppression at LHC from pQCD and AdS/CFT

Unexpected Event Characteristics … Conjecture: Large Extra Dimensions LHC will produce 100 (1) BH per second in pp (Au+Au) reactions at full energy For microscopic BHs,  ~ (M BH ) 3 ~ s, decays are essentially instantaneous T H ~ 1/R BH ~ GeV, so not just photons  q,g : l :  :,G = 75 : 15 : 2 : 8 Multiplicity ~ 5-20 Spherical events with leptons, many quark and gluon jets De Roeck (2002) Micro Black Holes at Colliders Dimopoulos, Landsberg, PRL (2001) Eardley, Giddings, PRD (2002) Bleicher, Hossenfelder, Stöcker, PLB(2002) Yoshino, Nambu, PRD (2003)

v 2 - scaling law recombination at hadronisation?

Statistical hadronization of charmonium states J/  : suppression at SPS/RHIC to enhancement at LHC J/Y yield at LHC charm production cross section at LHC Andronic et al., Nucl.Phys.A789:

master equation: master equation: J. Noronha-Hostler, C. Greiner, I. A. Shovkovy. Hagedorn gas close to Hagedorn spectrum:

Rapid kaon and baryon/antibaryon production J. Noronha-Hostler, C. Greiner, I. Shovkovy. (In Preparation)

Conclusions and Outlook Understanding the (perturbative and nonperturbative) QCD phenomena and properties of the QGP demands real time dynamics and full scope simulations of heavy ion collisions Understanding the very early stage of the reaction calls for a unified description of classical chromo fields and particles …the road of dissipative relativistic hydrodynamics What about hadronization and confinement …

Expansion velocity ~ 0.5 c at SPS ~0.7 at RHIC at SPS ??? at RHIC  B ~ 50 at RHIC  B ~ 250 at SPS  s ~ 1 at RHIC  s ~ 0.8 at SPS jets