Relativistic Hydrodynamics at RHIC and LHC Tetsufumi Hirano

Relativistic Hydrodynamics at RHIC and LHC Tetsufumi Hirano （平野哲文） （�京大学物理学院） References: T. Hirano, Prog. Theor. Phys. Supplement 168, 347(2007). T. Hirano, Nucl. Phys. A 805, 347 c(2008). International Workshop on Heavy Ion Physics at LHC Wuhan, China, May. 21 -24, 2008

Outline l Introduction l Dynamical modeling of heavy ion collisions l Bulk l Hard/rare probes and interplay btw. soft and hard l Summary and Outlook

Phase Diagram of QCD Understanding of phase diagram and EOS is one of the main topics in modern nuclear physics. Taken from http: //theory. gsi. de/~friman/trento_06. html

Constraint of EOS from Observation of Compact Stars Model EOS : Pressure as a function of mass-energy density Mass-Radius relation (Hydrostatic equilibrium) Observation of compact star mass TOV eq. plays an important role in understanding of EOS Taken from Lattimer, Prakash(’ 06) Tolman-Oppenheimer-Volkov eq.

Phase Diagram of QCD Taken from http: //theory. gsi. de/~friman/trento_06. html

Constraint of Cosmological Parameters from CMB “Best” cosmological parameters C. L. Bennett et al. , Ap. J. Suppl(’ 03) Observation COBE, WMAP, … CMB tools: CMBFAST, CAMB, … Taken from http: //lambda. gsfc. nasa. gov/ Analysis codes play a major role in precision physics.

Phase Diagram of QCD Taken from http: //theory. gsi. de/~friman/trento_06. html

“Mind The Gap” • The first principle (Quantum. Chromo Dynamics) • Inputs to phenomenology (lattice QCD) Complexity Non-linear interactions of gluons • Phenomenology (hydrodynamics) Strong coupling Dynamical many body system Color confinement • Experimental data @ Relativistic Heavy Ion Collider ~200 papers from 4 collaborations since 2000 ex. )QCDOC

Lessons from Other Fields phenomenology people experimental people lattice people l Necessity of collaborative activity in more extended community l Necessity of analysis tool(s) in R. H. I. C. physics l Toward establishment of the “observational QGP physics” l Era of discovery (RHIC) Era of precision physics (RHIC II & LHC)

Dynamical Modeling Based on 3 D Ideal Hydrodynamics

T. Hirano and Y. Nara(’ 02 -) CGC Geometric Scaling Shattering CGC “DGLAP region” Transverse momentum fluctuation Instability? Equilibration? Hydrodynamics • viscosity • non chem. eq. Proper time Dissipative “Perfect” hadron fluid gas QGP or GP Before Parton production collisions Preequilibrium Current Status of Dynamical Modeling in H. I. C. Hadronic cascade Low p. T Interaction (N)LOp. QCD Parton energy loss • Inelastic • Elastic Recombination Coalescence Fragmentation Intermediatep. T High p. T

BULK • 3 D Hydro+Cascade • CGC initial conditions

Full 3 D Hydro+Cascade Model Hadron gas via hadronic cascade model t QGP fluids via ideal hydrodynamics z 0 Glauber/ Color Glass Condensate* *See also talk by Klaus Werner with EPOS I. C.

TH et al. (’ 06). Centrality Dependence of v 2 Au. Au 200 Discovery of “large” v 2 at RHIC • v 2 data are comparable with hydro results for the first time. • Hadronic cascade models cannot reproduce data. This is the first time for ideal hydro at work in H. I. C. Strong motivation to develop hydro-based tools. Result from a hadronic cascade (JAM) (Courtesy of M. Isse)

TH(’ 02); TH and K. Tsuda(’ 02); TH et al. (’ 06). Pseudorapidity Dependence of v 2 Au. Au 200 QGP+hadron QGP only • v 2 data are comparable with 3 D hydro results again around h=0 • Not a QGP gas s. QGP* • Nevertheless, large discrepancy in forward/backward rapidity See next slides Note that the recent study of a parton cascade including gg ggg.

Importance of Hadronic “Corona” Au. Au 200 QGP fluid+hadron gas QGP+hadron fluids QGP only T. Hirano et al. , Phys. Lett. B 636(2006)299. • Boltzmann Eq. for hadrons instead of hydrodynamics • Including viscosity through finite mean free path Perfect fluid QGP core + Dissipative hadronic corona T. Hirano and M. Gyulassy, Nucl. Phys. A 769 (2006)71.

Highlights from a QGP Hydro + Hadronic Cascade Model Au. Au 200 b=7. 2 fm 0 -50% Adapted from. S. J. Sanders (BRAHMS) @ QM 2006 TH et al. , PRC 77, 044909(2008).

TH et al. , PRC 77, 044909(2008). Origin of Mass Ordering b=7. 2 fm Mass ordering behavior comes from hadronic rescattering. Not a direct signal of “perfect fluid QGP” Interplay btw. QGP fluid and hadron gas

Sensitivity to Initial Conditions Novel initial conditions from “Color Glass Condensate” lead to large eccentricity. Hirano and Nara(’ 04), Hirano et al. (’ 06) Kuhlman et al. (’ 06), Drescher et al. (’ 06) Need viscosity/soft EOS in QGP!

Excitation Function of v 2 Hadronic Dissipation • is huge at SPS. • still affects v 2 at RHIC. • is almost negligible at LHC. ~30% increase from RHIC to LHC

HARD/RARE PROBES • Hydro+Jet model • Hydro+J/Y model • Hydro+H. Q. model Interplay btw. soft and hard • Jet-fluid string formation

Utilization of Hydro Results Jet quenching Recombination J/psi suppression Heavy quark diffusion Coalescence Thermal radiation (photon/dilepton) Meson c J/psi c Baryon c bar Information along a path Information on surface Information inside medium *See also talk by Fu-Ming Liu

Jet Propagation through a QGP Fluid hydro+jet model Color: partondensity Plot: mini-jets T. Hirano and Y. Nara (’ 02 -) Full 3 D ideal hydrodynamics y + Au+Au 200 AGe. V, b=8 fm transverse plane@midrapidity Fragmentation switched off x PYTHIA Parton distribution fn. p. QCD 2 2 processes Fragmentation Gyulassy-Levai-Vitev formula Inelastic energy loss

p. T Distribution from Hydro+Jet Model Soft + Quenched Hard picture works reasonably well Re/Co components may be needed for a better description Note: Hadronic cascade is switched off in the bulk T. Hirano and Y. Nara, Phys. Rev. C 69, 034908(2004).

Back-To-Back Correlation Not only energy loss but also deflection are found to be important. T. Hirano and Y. Nara, Phys. Rev. Lett. 91, 082301(2003).

Gunji, Hamagaki, Hatsuda, Hirano, PRC 76, 051901(2007). Onset of J/Y Melting in a QGP Fluid Suppression factor of J/ Y Hydro+J/Y model J/psi c c bar J/Y is assumed to melt away above TJ/y ~ 2 Tc Local temperature from full 3 D hydro simulations

Heavy Quark Diffusion in a QGP Fluid Hydro+H. Q. model c c-bar v 2 is sensitive to relaxation time for heavy quarks in QGP. Toward comprehensive understanding of transport properties of QGP Akamatsu, Hatsuda, Hirano (in preparation)

Hadronization through Jet. Fluid String Formation Space-time evolution of the QGP fluid Open data table http: //tkynt 2. phys. s. u-tokyo. ac. jp /~hirano/parevo. html Energy loss GLV 1 st order String Fragmentation PYTHIA (Lund) Hirano, Isse, Nara, Ohnishi, Yoshino, Mizukawa, nucl-th/0702068; 0805. 2795[nucl-th].

Summary & Outlook l Development of an analysis code in H. I. C. based on relativistic hydrodynamics l Glauber I. C. + QGP fluid + hadronic gas picture works well l Sensitivity to initial conditions in hydro? l Application of hydro results l Single- and di-hadron distributions at high p. T l J/Y suppression & heavy quark diffusion l Jet-Fluid String formation l EM probes l Toward an open and standard tool in H. I. C. in the upcoming era of precision physics (like PYTHIA, CMBFAST, …)

Thanks!