QGP hydro + hadronic cascade model: Status report Tetsufumi Hirano Dept. of Physics The Univ. of Tokyo RCNP, Oct , 2007 TH, U.Heinz, D.Kharzeev, R.Lacey and Y.Nara, PLB636(2006)299; in preparation TH, U.Heinz, work in progress.

Outline Introduction Momentum Space (elliptic flow) Mass ordering of v 2 (p T ) revisited Violation of mass ordering for  mesons Soft EOS in CGC case? Configuration Space (femtoscopy) Source functions from hydro + cascade 1D, 3D (r side, r out, r long )-directions Summary

Motivation To understand the QGP in H.I.C., one needs to develop a dynamical framework. One example of agreement btw. data and theory is not sufficient. (Concerning accidental reproduction) One needs to improve his/her model continuously toward establishment of the “observational QGP physics”.

Mechanism of Mass Ordering? STAR white paper (’05) PHENIX white paper (’05) Lines: Results from Ideal hydro

A Hybrid Approach: QGP hydro + hadronic cascade 0 collision axis time Au QGP fluid Initial condition: Transverse  Glauber Longitudinal  “BGK triangle” QGP fluid: 3D ideal hydrodynamics (Hirano) massless free u,d,s+g gas + bag const. T c = 170 MeV Hadron gas: Hadronic cascade, JAM1.09 (Nara) T sw = 169 MeV hadron gas TH et al.(’06) (1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.

Pseudorapidity Distribution Tune initial parameters with T th = 100MeV to reproduce dN/deta. Then, switch to hadronic cascade below T=T sw. Caveat: Rejecting in- coming particles at T sw

p T spectra for pi, K, and p Reasonable reproduction of yields and spectra in low p T region (p T <~1.5 GeV/c) TH et al. (in preparation).

v 2 (p T ) for pi, K, and p OK! Fail to reproduce data due to (absence of) fluctuation of geometry Miller&Snelling (’03), Bhalerao&Ollitrault(’06) Andrade et al (’06),Drescher&Nara (’07) Browniowski et al(’07) TH et al. (in preparation).

Hydro + Cascade at Work in Forward Rapidity Regions Adapted from S.J.Sanders QM2006

Origin of Mass Ordering Mass ordering behavior results from hadronic rescatterings.  Not a direct signal of “perfect fluid QGP”  Interplay btw. ideal QGP fluid and dissipative hadron gas TH and M.Gyulassy; TH et al. (in preparation). b=7.2fm

Why they shift oppositely? protonspions pTpT v 2 (p T ) v2v2 must decrease with proper time v 2 for protons can be negative even in positive elliptic flow TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01); TH et al, in preparation

 MESON FLOW

What happens to strangeness sector?

Additive Quark Model in Transport Codes (JAM/RQMD/UrQMD) For cross sections without exp. data, Expected to be very small for phi, Omega, etc.

Distribution of Freeze-Out Time b=2.0fm (no decay) TH et al. (in preparation). Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98)

 -meson case in p T < 1 GeV/c Just after hadronization Final results T = T sw = 169 MeV b=7.2fm TH et al. (in preparation). Caveat: Published PHENIX data obtained in p T >~1GeV/c for  mesons This is NOT obtained within ideal hydrodynamics.

What happens if  -meson follows radial flow? Of course, mass ordering is seen in hydro calculations

CGC INITIAL CONDITIONS

CGC Initial Condition Unintegrated gluon distribution a.la. Kharzeev, Levin, and Nardi Gluon production via k T factorization formula Count deposited energy in dV at (  0,x,y,  s ),  0 = 0.6fm/c Transverse profile: Entropy density Longitudinal Profile: Brodsky-Gunion-Kuhn triangle Color Glass CondensateGlauber-BGK type ss x(fm) ss ene.density

Two Hydro Initial Conditions Which Clear the “First Hurdle” 1. CGC model Matching I.C. via e(x,y,  ) 2.Glauber model (as a reference) N part :N coll = 85%:15% Centrality dependenceRapidity dependence Kharzeev,Levin, and Nardi Implemented in hydro by TH and Nara

v 2 (N part ) from CGC + QGP Fluid + Hadronic Gas Model Glauber: Early thermalization Discovery of Perfect Fluid QGP CGC: No perfect fluid? Additional viscosity required in QGP Important to understand initial conditions much better for making a conclusion TH et al.(’06) Adil, Gyulassy, Hirano(’06)

Large Eccentricity from CGC Initial Condition x y Pocket formula (ideal hydro): v 2 ~ 0.2 RHIC Ollitrault(’92) Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06)

Soft QGP EoS Soft EOS? (equilibrium) or Viscosity? (non-eq.) Soft EoS reduces v 2 as it should

Summary of flow part A QGP fluid with hadronic rescattering Origin of mass ordering for v 2 (p T )  Radial flow effect, not “ mass effect ”. Violation of mass ordering for  mesons Mass ordering itself is not a direct signal of perfect fluidity! Interplay btw. QGP fluids and hadron gases. CGC I.C. is “ eccentric ”. Soft EOS is needed within ideal hydrodynamics.

Femtoscopy from Hydro + Cascade From momentum space to configuration space

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

Distribution of the Last Interaction Point from Hydro + Cascade Blink: Ideal Hydro, Kolb and Heinz (2003) x-t x-y p x ~ 0.5 GeV/c for pions Long tail (  decay? elastic scattering?) Positive x-t correlation

1D Source Function from Hydro + Cascade 0.48 < K T <0.6 GeV/c0.2 < K T <0.36 GeV/c Angle averaged source function Broader than PHENIX data Almost no K T dependence  PHENIX data Significant effects of hadronic rescatterings K T =P T /2

Omega Decay or Not? Switch off omega decay by hand in hadronic cascade  Long tail still seen.  Soft elastic scattering of pions? b=5.8fm

3D Source Function from Hydro + Cascade (preliminary!) side outlong Source function in PCMS 1fm-slice in each direction 0.2<K T <0.4 GeV/c, |  | < 0.35,  + -  +,  - -  - pairs Red: Without rescattering, Black: With rescattering No longer Gaussian shape (Lines: Gaussian) Broaden by hadronic rescatterings

Summary of Femtoscopy 1D- and 3D-source functions from a dynamical model (QGP hydro + hadronic cascade) Significant rescattering effects are seen. Source function is no longer Gaussian. Long tail in 1D source function is described within hadronic rescatterings. K T dependence?

Outlook Pair-angle dependence of source function in non-central collisions Other pairs (K, p, ,…)  correlation to investigate  interaction (with Ohnishi-san) Just get started. Many other things to do…