Seminar @ YITP 12/10/2008 Dynamical Modeling of Heavy Ion Collisions Tetsufumi Hirano Department of Physics The University of Tokyo OUTLINE • Introduction • Basic Checks of observables – Energy density – Chemical and kinetic equilibrium • Dynamics of Heavy Ion Collisions – Hydrodynamic modeling – Elliptic flow • Towards precision physics of QGP – Jet quenching (Transport coefficient) – J/psi suppression • Summary and Outlook Two Faces of QCD Confinement Asymptotic free q-qbar potential Running coupling of QCD Physics depends on (energy) scale. Recipe for QGP Compress and/or Heat-up! •Density (chemical potential) scale •Temperature scale History of the Universe ~ History of Matter Quark Gluon Plasma Hadronization Nucleosynthesis QGP study Understanding early universe Little Bang! Relativistic Heavy Ion Collider(2000-) RHIC as a time machine! STAR front view STAR Collision energy 100 GeV per nucleon Au(197×100)+Au(197×100) Multiple production (N~5000) Heat side view Dynamics of Heavy Ion Collisions Dynamics of Heavy Ion Collisions Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons) Time scale Temperature scale 10fm/c~10-23sec 100MeV~1012K <<10-4(early universe) y Ncoll & Npart Thickness function: Woods-Saxon nuclear density: # of binary collisions x Gold nucleus: r0=0.17 fm-3 R=1.12A1/3-0.86A-1/3 d=0.54 fm # of participants sin = 42mb @200GeV 1－（survival probability） Centrality Npart and Ncoll as a function of impact parameter PHENIX: Correlation btw. BBC and ZDC signals Elliptic Flow What is Elliptic Flow? Ollitrault (’92) How does the system respond to spatial anisotropy? No secondary interaction Hydro behavior y f x INPUT Spatial Anisotropy 2v2 OUTPUT dN/df dN/df Interaction among produced particles Momentum Anisotropy 0 f 2p 0 f 2p v2 from a Boltzmann simulation Zhang et al.(’99) ideal hydro limit v2 : Ideal hydro b = 7.5fm : strongly interacting system t(fm/c) generated through secondary collisions v2 is saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity) Why Hydrodynamics? Once one accepts local thermalization ansatz, life becomes very easy. Energy-momentum: Conserved number: Dynamic Phenomena in HIC •Expansion, Flow •Space-time evolution of thermodynamic variables Static •EoS from Lattice QCD •Finite T, m field theory •Critical phenomena •Chiral property of hadron Why Hydrodynamics? (contd.) • We would like to understand the QCD matter under equilibrium. • Lattice QCD is not able to describe dynamics of heavy ion collisions. • Analyze heavy ion reaction based on a model with an assumption of local equilibrium, and see what happens and whether it is consistent with data. • If consistent, it would be a starting point of the physics of QCD matter. Dynamics of Heavy Ion Collisions Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons) Inputs in hydrodynamic simulations: •Initial condition •Equation of state •Decoupling prescription Recent Hydro Results from Our Group QGP fluid + hadronic cascade time hadron gas QGP fluid collision axis 0 Au Au Initial condition (t=0.6fm) 1. Glauber model 2. (CGC model) QGP fluid: 3D ideal hydrodynamics (Tc = 170 MeV) Massless free u,d,s+g gas + bag const. Hadron phase: 1. Tth=100MeV 2. Hadronic cascade (JAM) (Tsw = 169 MeV) Hybrid approaches: (1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak (3D) Nonaka, Bass, Hirano et al. Inputs to Hydro: Multiplicity Centrality dependence 1.Glauber model Npart:Ncoll = 85%:15% 2. CGC model Matching I.C. via e(x,y,hs) Rapidity dependence Kharzeev, Levin, and Nardi Implemented in hydro by TH and Nara pT Spectra for PID hadrons A hybrid model works well up to pT~1.5GeV/c. Other components (reco/frag) would appear above. Centrality Dependence of v2 TH et al. (’06). Discovery of “Large” v2 at RHIC • v2 data are comparable with hydro results. • Hadronic cascade cannot reproduce data. • Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations. Result from a hadronic cascade (JAM) (Courtesy of M.Isse) Pseudorapidity Dependence of v2 TH(’02); TH and K.Tsuda(’02); TH et al. (’06). QGP+hadron QGP only h<0 h=0 h>0 •v2 data are comparable with hydro results again around h=0 •Not a QGP gas sQGP •Nevertheless, large discrepancy in forward/backward rapidity See next slides Hadron Gas Instead of Hadron Fluid T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71. A QGP fluid surrounded by hadronic gas QGP core QGP: Liquid (hydro picture) Hadron: Gas (particle picture) “Reynolds number” Matter proper part: (shear viscosity) (entropy density) big in Hadron small in QGP Importance of Hadronic “Corona” QGP fluid+hadron gas QGP+hadron fluids QGP only •Boltzmann Eq. for hadrons instead of hydrodynamics •Including viscosity through finite mean free path •Suggesting rapid increase of entropy density •Deconfinement makes hydro work at RHIC!? Signal of QGP!? T.Hirano et al.,Phys.Lett.B636(2006)299. QGP Liquid + Hadron Gas Picture Works Well 20-30% Mass dependence is o.k. Note: First result was obtained by Teaney et al. •Centrality dependence is ok •Large reduction from pure hydro in small multiplicity events T.Hirano et al.,Phys.Lett.B636(2006)299; Phys.Rev.C77,044909(2008). Centrality Dependence of Differential v2 PHENIX Pions, AuAu 200 GeV PHENIX Hybrid Model at Work at sqrt(sNN)=62.4 GeV PHENIX PHENIX Pions, AuAu 62.4 GeV Differential v2 in Au+Au and Cu+Cu Collisions Au+Au Cu+Cu Same Npart, different eccentricity Au+Au Cu+Cu Same eccentricity, different Npart Eccentricity Fluctuation Adopted from D.Hofman(PHOBOS), talk at QM2006 Yi Y0 A sample event from Monte Carlo Glauber model Interaction points of participants vary event by event. Apparent reaction plane also varies. The effect is significant for smaller system such as Cu+Cu collisions Initial Condition with Fluctuation Throw a dice to choose b: bmin<b<bmax Rotate each Yi to Ytrue E.g.) bmin= 0.0fm bmax= 3.3fm in Au+Au collisions at 0-5% centrality average over events average over events Effect of Eccentricity Fluctuation on v2 (Glauber) AuAu CuCu v2(w.rot) ~ 2 v2(w.o.rot) at Npart~350 in AuAu v2(w.rot) ~ 4 v2(w.o.rot) at Npart~110 in CuCu Significant effects of fluctuation! Effect of Eccentricity Fluctuation on v2 (CGC) AuAu CuCu CGC + QGP with (small) viscosity + hadronic gas!? Toward precision physics of QGP Lesson from Observational Cosmology “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. Hydrodynamic model in H.I.C. Tomography CT (computed tomography) scan “Tomography” 1. Known probes: Spectra reliably calculable via pQCD 2. Good detector: RHIC experiments! 3. Interaction btw. probes and unknowns: Recent development in this field *平野哲文、浜垣秀樹、「ジェットで探るクォークグルーオンプラズマ」、日本物理学会誌2004年12月号 Jet Tomography Tool 1. Jet quenching g 180 deg. correlation? Bjorken(’82) Gyulassy,Plüme Wang (’90) g g High “density” matter Tool 2. Jet acoplanarity Bjorken(’82) Appel (’86) Blaizot & McLerran (’86) Difference btw. pp and AA AA collisions pp collisions QGP? Nucleon Jet f a c D A× f’ a s Nucleon b f c D d D s d D f: Parton distribution D: Fragmentation function A× f’ b RAA Nuclear Modification Factor 1 0.341 (null result) binary collision scaling Au+Au 0-10% central •b=2.8 fm •Ncoll = 978 •Npart = 333 participant scaling •Npart/Ncoll = 0.341 pT “Transport Coefficient” R.Baier, hep-ph/0209038 For static medium, Baier et al. for pQCD Stopping power One of the important quantity to characterize the QGP RAA for p0 and IAA for charged How do we understand this large K? J/psi Suppression Quarkonium suppression in QGP Color Debye Screening T.Matsui & H. Satz PLB178 416 (1986) Suppression depends on temperature (density) and radius of QQbar system. c c Color Screening TJ/psi : 1.6Tc~2.0Tc Tc, Ty’ : ~ 1.1Tc May serve as the thermometer in the QGP. M.Asakawa and T.Hatsuda, PRL. 92, 012001 (2004) A. Jakovac et al. PRD 75, 014506 (2007) G.Aarts et al. arXiv:0705.2198 [hep-lat]. (Full QCD) See also T.Umeda,PRD75,094502(2007) Results from Hydro + J/psi Model 8 • Best fit @ (TJ/y, Tc, fFD) = (2.00Tc, 1.34Tc, 10%) 1s 2s Bar: uncorrelated sys. Bracket: correlated sys. Contour map • Onset of J/y suppression at Npart ~ 160. ( Highest T at Npart~160 reaches to 2.0Tc.) • Gradual decrease of SJ/ytot above Npart~160 reflects transverse area with T>TJ/y increases. • TJ/y can be determined in a narrow region. T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007 Summary and Outlook • Elliptic flow – QGP fluid + hadron gas picture works well. – Starting Point of finite temperature QCD in H.I.C. • Tomography utilizing hydro model – Statistical analysis of jet quenching parameter (stopping power of high energy partons) – J/psi suppression above T~2Tc. (Melting temperature of charmonium) • Toward establishment of the “observational QGP physics”.
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