Hydrodynamics in Heavy Ion Collisions and QCD Equation

Hydrodynamics in Heavy Ion Collisions and QCD Equation of State Current status of a 3 D hydro+cascade model Tetsufumi Hirano Department of Physics The University of Tokyo References: T. Hirano, U. W. Heinz, D. Khaezeev, R. Lacey, Y. Nara Phys. Lett. B 636, 299 (2006); J. Phys. G 34, S 879 (2007); ar. Xiv: 0710. 5795 [nucl-th] (Phys. Rev. C, in press. ). T. Hirano, U. Heinz, (work in progress).

A Remark at the Beginning Hydrodynamic Model ≠Hydrodynamics So far, discovery of the perfect fluid QGP has been made by one particular modeling of relativistic hydrodynamics. How robust/fragile is the discovery? See, Huovinen’s talk

Inputs for Hydrodynamic Simulations for Perfect Fluids Final stage: Free streaming particles Need decoupling prescription t z 0 Intermediate stage: Hydrodynamics can be valid as far as local thermalization is achieved. Need EOS P(e, n) Initial stage: Particle production, pre-thermalization? Instead, initial conditions for hydro simulations

time Our Strategy: QGP fluid + hadronic cascade in full 3 D space hadron gas QGP fluid collision axis 0 Au Au Initial condition : 1. Glauber model 2. CGC model QGP fluid: 3 D ideal hydrodynamics (Tc = 170 Me. V) 1. massless free u, d, s+g gas + bag const. 2. Soft Eo. S Hadronphase: 1. Tth=100 Me. V 2. Hadronic cascade (Tsw = 169 Me. V) Hybrid approaches: (1 D) Bass, Dumitru (2 D) Teaney, Lauret, Shuryak, (3 D) Nonaka, Bass, Hirano et al.

Two Hydro Initial Conditions Which Clear the “First Hurdle” Centrality dependence Rapidity dependence 1. Glauber model Npart: Ncoll = 85%: 15% 2. CGC model Matching I. C. via e(x, y, hs) Kharzeev, Levin, and Nardi Implemented in hydro by TH and Nara

QGP fluid+hadron gas with Glauber I. C. p. T Spectra for PID hadrons A hybrid model works well up to p. T~1. 5 Ge. V/c. Other components (reco/frag) would appear above.

QGP+hadron fluids with Glauber I. C. TH et al. (’ 06) Centrality Dependence of v 2 • v 2 data are hadronic cascade result (Courtesy of M. Isse) comparable with hydro results. • Hadronic cascade cannot reproduce data. • Note that, in v 2 data, there exists eccentricity fluctuation which is not considered in model calculations.

QGP+hadron fluids with Glauber I. C. Pseudorapidity Dependence of v 2 QGP+hadron QGP only h<0 h=0 h>0 • v 2 data are comparable with hydro results again around h=0 • Not a QGP gas s. QGP • Nevertheless, large discrepancy in forward/backward rapidity TH(’ 02); TH and K. Tsuda(’ 02); TH et al. (’ 06).

QGP fluid+hadron gas with Glauber I. C. Importance of Hadronic “Corona” 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 effective viscosity through finite mean free path

QGP fluid+hadron gas with Glauber I. C. Differential v 2, centrality dependence 20 -30% Mass dependence is o. k. Note: First result was obtained by Teaney et al. T. Hirano et al. (’ 07) • Centrality dependence is ok • Large reduction from pure hydro in small multiplicity events

QGP fluid+hadron gas with Glauber I. C. Differential v 2 in Forward hybrid model AMPT Adopted from S. J. Sanders (BRAHMS) talk @ QM 2006

QGP fluid+hadron gas with Glauber I. C. Mass Ordering for v 2(p. T) Pion 20 -30% Proton Mass dependence is o. k. from hydro+cascade. Mass ordering comes from hadronic rescattering effect. Interplay btw. radial and elliptic flows.

QGP fluid+hadron gas with Glauber I. C. f-meson case Just after hadronization b=7. 2 fm Final results b=7. 2 fm T = Tsw = 169 Me. V in p. T < 1 Ge. V/c Violation of mass ordering for phi mesons! Clear signal of early decoupling! Caveat: Published PHENIX data obtained in p. T>~1 Ge. V/c for f mesons

QGP fluid+hadron gas with Glauber I. C. Centrality Dependence of Differential v 2 PHENIX Pions, Au. Au 200 Ge. V Thanks to M. Shimomura (Tsukuba)

QGP fluid+hadron gas with Glauber I. C. Hybrid Model at Work at sqrt(s. NN)=62. 4 Ge. V PHENIX Pions, Au. Au 62. 4 Ge. V Thanks to M. Shimomura (Tsukuba)

QGP fluid+hadron gas with Glauber I. C. Differential v 2 in Au+Au and Cu+Cu Collisions Au+Au Cu+Cu Same Npart, different eccentricity Au+Au Cu+Cu Same eccentricity, different Npart

QGP fluid+hadron gas with Glauber I. C. Distribution of the Last Interaction Point from Hydro + Cascade x-t x-y px ~ 0. 5 Ge. V/c for pions • Long tail (w decay? elastic scattering? ) • Positive x-t correlation Blink: Ideal Hydro, no resonance decays Kolb and Heinz (2003)

QGP fluid+hadron gas with Glauber I. C. 1 D (Angle-averaged) Source Function from Hydro + Cascade KT=PT/2 0. 2 < KT <0. 36 Ge. V/c 0. 48 < KT <0. 6 Ge. V/c • Broader than PHENIX data • Almost no KT dependence ? PHENIX data • Significant effects of hadronic rescatterings PHENIX, PRL 98, 132301(2007); ar. Xiv: 0712. 4372[nucl-ex]

Summary So Far • A hybrid approach (QGP fluid + hadronic cascade) initialized by Glauber model works quite well. • (KT dependence of source size? ) • So far, so good. • What happens if initial condition is changed?

Eccentricity from CGC Initial Condition y x Hirano et al. (’ 06). Kuhlman et al. (’ 06), Drescher et al. (’ 06). See also, Lappi, Venugopalan (’ 06) Drescher, Nara (’ 07)

QGP fluid+hadron gas with CGC I. C. v 2 Depends on Initialization TH et al. (’ 06) Glauber: ü Early thermalization ü Discovery of Perfect Fluid QGP CGC: ü No perfect fluid? ü Additional viscosity required in QGP? Important to understand initial conditions much better for making a conclusion Adil, Gyulassy, Hirano(’ 06)

QGP fluid+hadron gas with CGC I. C. Soft Eo. S or Viscosity? v 2 is sensitive to sound velocity. Soft Eo. S in the QGP phase leads to reasonable reproduction of v 2 Again, importance of understanding initial conditions. Imprement of Lattice Eo. S?

Summary and Outlook • Success and challenge of a hydro + cascade model – Glauber + hard QGP Eo. S + hadronic afterburner – CGC + soft QGP Eo. S + hadronic afterburner • Future studies Higher Tc, Tsw or Lattice Eo. S Fluctuation of initial geometry

Why they shift oppositely? protons v 2(p. T) pions <p. T> p. T must decrease with proper time v 2 for protons can be negative even in positive elliptic flow TH and M. Gyulassy, NPA 769, 71(06) P. Huovinen et al. , PLB 503, 58(01)

What happens to strangeness sector?

Distribution of Freeze-Out Time (no decay) b=2. 0 fm Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’ 98) Phi can serve a direct information at the hadronization.

phi/p Ratio as a function of p. T • pp collisions • Pure hydro in AA collisions • Hydro + cascade in AA collisions Clear signal for early decoupling of phi mesons

Recent Results from Lattice 1 16 81 e (Ge. V/fm 3) Max e 0 ~ 45 Ge. V/fm 3 in hydro at RHIC Ave. e 0 ~ 13 Ge. V/fm 3 M. Cheng et al. , Phys. Rev. D 77, 014511 (2008).

Source Imaging Koonin-Pratt eq. (Koonin(’ 77), Pratt(’ 84)): Primed quantities in Pair Co-Moving System (PCMS) (P = 0) Source function and normalized emission rate Source Imaging: (Brown&Danielewicz (’ 97 -)) Inverse problem from C to D with a kernel K No more Gaussian parameterization!

Long Tail Attributable to w Decay ? b=5. 8 fm Plot: PHENIX Hist. : Hydro+cascade w/o w decay No! Switch off omega decay by hand in hadronic cascade Long tail is still seen. Soft elastic scattering of pions?

3 D Source Function from Hydro + Cascade side out long • Source function in PCMS • 1 fm-slice in each direction • 0. 2<KT<0. 4 Ge. V/c, |h| < 0. 35, p+-p+, p--p- pairs • Black: With rescattering, Red: Without rescattering • No longer Gaussian shape (Lines: Gaussian) • Significantly broadened by hadronic rescatterings