Hirano-RBRC

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					       “RHIC Physics in the Context of the Standard Model”
              RBRC workshop on Heavy Ion Physics




            Perfect Fluid QGP
                 or CGC?
                  Tetsufumi Hirano*
       Institute of Physics, University of Tokyo
                                             * Visiting scientist at RBRC
References:
T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.
T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299;
work in progress.
OUTLINE

• Dynamical modeling in heavy ion collisions
  based on ideal hydrodynamics
• Elliptic flow and perfect fluid
• Results from hydro models
  – Dependence on freezeout prescription
  – Dependence on initialization
• Summary and Outlook
  Why Hydrodynamics?
Once one accepts local      Static
                            •EoS from Lattice QCD
thermalization ansatz,
                            •Finite T, m field theory
life becomes very easy.     •Critical phenomena
                            •Chiral property of hadron
Energy-momentum:

Conserved number:

 Dynamic Phenomena in HIC
 •Expansion, Flow
                            A possible mechanism of
 •Space-time evolution of
                            apparent thermalization
  thermodynamic variables
                                Talk by Y.Nara
Three Inputs for Hydrodynamic
Models
                              Final stage:
                              Free streaming particles
           t                   Need decoupling prescription
                              Intermediate stage:
                              Hydrodynamics can be valid
                              as far as local thermalization is
                              achieved.  Need EoS P(e,n)
                          z
               0              Initial stage:
                              Particle production,
Need modeling                 pre-thermalization, instability?
(1) EoS, (2) Initial cond.,   Instead, initial conditions
and (3) Decoupling             are put for hydro simulations.
  Intermediate Stage: Equation of
  State                Typical EoS in hydro models
       Lattice QCD simulations




                                                                                P.Kolb and U.Heinz(’03)
                                                         H: resonance gas(RG)




                                 F.Karsch et al. (’00)
                                                         Q: QGP+RG




Recent lattice results at finite T
                                        Latent heat
 Talk by Y.Aoki
      Lattice QCD predicts cross over phase transition.
      Nevertheless, energy density explosively increases
      in the vicinity of Tc.  Looks like 1st order.
Initial Stage: Initial Condition
            Energy density distribution




    Transverse plane            Reaction plane
Parameterization/model-calculation to reproduce
         (dN/dh)/(Npart/2) and dN/dh
  Final Stage: Freezeout
(1) Sudden freezeout             (2) Transport of hadrons
                       T=Tf      via Boltzman eq. (hybrid)
             t                                t

        Hadron fluid


          QGP fluid                         QGP fluid

                             z                               z
                 0                                 0

At T=Tf,                         Continuum approximation no
l=0 (ideal fluid)                longer valid at the late stage
 l=infinity (free stream)       Molecular dynamic approach
                                 for hadrons (p,K,p,…)
Caveats on Hydrodynamic Results
     Obviously, final results depend on
modeling of
   1.Equation of state
   2.Initial condition
   3.Freezeout
So it is indispensable to check sensitivity
of conclusion to model assumptions and
try to reduce model parameters.
In this talk, I will cover 2 and 3.
        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
                                   Interaction among                               2v2
                                   produced particles
dN/df




                                                          dN/df
                                    OUTPUT
                               Momentum Anisotropy
        0        f        2p
                                                                  0       f         2p
     Elliptic Flow from a Kinetic Theory
Zhang et al.(‟99)             ideal hydro limit
                                                    View from collision axis
       Time evolution of v2
                                                            b = 7.5fm
v2




                                                  • Gluons uniformly distributed
                                                  in the overlap region
                                                  • dN/dy ~ 300 for b = 0 fm
                                                  • Thermal distribution with
                    t(fm/c)                       T = 500 MeV

       generated through secondary collisions
 v2 is saturated in the early stage
       sensitive to cross section (~m.f.p.~viscosity)
Basis of the Announcement
        STAR(‟02)                 PHENIX(‟03)




                                pT dependence
 Multiplicity dependence        and mass ordering

       Hydro results: Huovinen, Kolb, Heinz,…
Sensitivity to Different Assumptions
in Early/Late Stages
        Initial
        Condition                      Color Glass
                     Glauber-type
                                       Condensate
 Freezeout


                                           ?
    Sudden            Discovery of
   freezeout        “Perfect Liquid”

    Hadronic
  rescattering            ?                ?
   Dependence on
Freezeout Prescription



   T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.
Classification of Hydro Models
                                                            Model HC:
     T                Model CE:          Model PCE:
                                                         Teaney, Shuryak,
                   Kolb, Huovinen,     Hirano, Teaney,
                                                          Bass, Dumitru,
                   Heinz, Hirano…          Kolb…
     QGP phase



                                                                …
                                                                            ~1 fm/c

                       Perfect Fluid of QGP
Tc                                                                          ~3 fm/c
                                     Tch Partial
                       Chemical                           Hadronic
                                           Chemical
                       Equilibrium                        Cascade
                                           Equilibrium
                        EOS
                                            EOS
                 Tth                 Tth                                    ~10-15
                                                                                fm/c
                                                                            t
                       ideal hydrodynamics
v2(pT) for Different Freezeout
Prescriptions
                           2000 (Heinz, Huovinen, Kolb…)
                           Ideal hydro w/ chem.eq.hadrons
                           2002 (TH,Teaney,Kolb…)
                           +Chemical freezeout
                           2002 (Teaney…)
                           +Dissipation in hadron phase
                           2005 (BNL)
                           “RHIC serves the perfect liquid.”

                20-30%



          Why so different/similar?
         Accidental Reproduction of v2(pT)
v2(pT)




                                              v2(pT)
          At hadronization                              Chemical Eq.
 v2




                                               v2
                                  freezeout
                <pT>         pT                            <pT>        pT




                                              v2(pT)
                                                       Chemical F.O.



                                               v2



                                                           <p >
Why <pT> behaves differently?
                                                            Mean ET
Chemical    ET per particle increases                       decreases
Freezeout    in chemical equilibrium.                       due to pdV
                                                            work
 This effect delays cooling of the system
                like a viscous fluid.
              Chemical equilibrium
                  imitates viscosity    MASS energy
           at the cost of particle yield!
 Chemical
    Hydro+Cascade is the only model to
Equilibrium
                                          KINETIC
                 reproduce v2(pT)!!!       energy

       For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71
v2(pT) for identified hadrons
from QGP Hydro + Hadronic Cascade


                                         Pion
                      20-30%

                                                Proton



Mass dependence is o.k.           Mass splitting/ordering comes
Note: First result was obtained   from hadronic rescattering.
by Teaney et al.                  Not a direct signature of
                                  perfect fluid QGP
v2(Npart) and v2(eta)




   Significant Hadronic Viscous Effects
            at Small Multiplicity!
Summary So Far

• When we employ Glauber-type initial
  conditions, hadronic dissipation is
  indispensable.
• Perfect fluid QGP core and dissipative
  hadronic corona
   Dependence on
Initialization of Hydro



     T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara,
     Phys.Lett.B 636 (2006)299; work in progress.
(1) Glauber and (2) CGC Hydro Initial
Conditions Which Clear the First Hurdle
Centrality dependence           Rapidity dependence




 •Glauber model
   Npart:Ncoll = 85%:15%
 •CGC model                          Details on CGC
   Matching I.C. via e(x,y,h)         Talk by K.Itakura
                                            TH et al.(’06)
v2(Npart) from
QGP Hydro + Hadronic Cascade
                                 Glauber:
                                  Early thermalization
                                  Mechanism?
                                 CGC:
                                  No perfect fluid?
                                  Additional viscosity
                                    is required in QGP



Importance of better understanding of initial condition
Large Eccentricity from CGC Initial
Condition           Hirano and Nara(’04), Hirano et al.(’06)
                             Kuhlman et al.(’06), Drescher et al.(’06)

          y



                       x




        Pocket formula (ideal hydro):
         v2 ~ 0.2e @ RHIC energies
                                           Ollitrault(’92)
v2(pT) and v2(eta) from CGC initial
conditions



              20-30%




          v2(model) > v2(data)
Summary and Outlook




• Much more studies needed for initial states
• Still further needed to investigate EOS
  dependence
• To be or not to be (consistent with hydro),
  that is the question!
Acknowledgement
                        Miklos is supposed
                        to attend this
                        workshop but
                        cannot come.
                        I really appreciate
                        his continuous
                        encouragement
                        to my work.

   Get well soon completely, Miklos!
Excitation Function of v2

                   Hadronic Dissipation
                   •is huge at SPS.
                   •still affects v2 at RHIC.
                   •is almost negligible at LHC.
Source Function from 3D Hydro +
Cascade
          How much the source function
             differs from ideal hydro
             in Configuration space?




   Blink: Ideal Hydro, Kolb and Heinz (2003)
   Caveat: No resonance decays in ideal hydro
Non-Gaussian Source?




                 y


                           p x=
                       x   0.5GeV/c
Viscosity from a Kinetic Theory
                                See, e.g. Danielewicz&Gyulassy(’85)

For ultra-relativistic particles, the shear viscosity is



                                           Ideal hydro:
                                               l0


                                     shear viscosity  0
 Transport cross section
  Viscosity and Entropy
•Reynolds number                                                              Iso, Mori, Namiki (‟59)

                                                                               R>>1
                                                                               Perfect fluid
     where


•1+1D Bjorken flow                Bjorken(’83)
Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…

                                                                                   (Ideal)
                                                                                  (Viscous)
     h : shear viscosity (MeV/fm2), s : entropy density (1/fm3)
          h/s is a good dimensionless measure
    (in the natural unit) to see viscous effects.
Why QGP Fluid + Hadron Gas Works?
                        h : shear viscosity, s : entropy density
TH and Gyulassy (‟06)




                                                    Kovtun,Son,Starinets(’05)
               •Absolute value of viscosity   •Its ratio to entropy density
                                        !
                        Rapid increase of entropy density can
                             make hydro work at RHIC.
                               Deconfinement Signal?!
Temperature Dependence of h/s
•Shear Viscosity in Hadron Gas           Danielewicz&Gyulassy(‟85)




•Assumption: h/s at Tc in the sQGP is 1/4p
                                             Kovtun, Son, Starinets(„05)




            No big jump in viscosity at Tc!
•We propose a possible scenario:
                                                      [Pa] = [N/m2]
Digression
        (Dynamical) Viscosity h:
          ~1.0x10-3 [Pa s] (Water 20℃)
          ~1.8x10-5 [Pa s] (Air 20℃)
        Kinetic Viscosity n=h/r:
          ~1.0x10-6 [m2/s] (Water 20℃)
          ~1.5x10-5 [m2/s] (Air 20℃)

 hwater > hair BUT nwater < nair
Non-relativistic Navier-Stokes eq. (a simple form)



                  Neglecting external force and assuming incompressibility.
          A Bigger Picture in Heavy Ion
          Collisions
                   QGP or GP production collisions
                                               Before




                                                          CGC             Geometric Scaling       “DGLAP region”
                                   equilibrium



                                                                                               Transverse momentum
                                                             Shattering CGC                        (N)LOpQCD
       Dissipative “Perfect” fluid Parton

                                   Pre-




                                                          Instability?
                                                          Equilibration?
                                                                                                 Parton energy loss
                                                        Hydrodynamics                            •Inelastic
                                                                               Interaction       •Elastic
                                                        •viscosity?
                                                        •non chem. eq.?
                                                                              Recombination
                                                                               Coalescence
       hadron




                                                          Hadronic
Proper time




                                                                                                  Fragmentation
       gas




                                                          cascade

                                                           Low pT            Intermediate pT           High pT
                      Differential Elliptic Flow Develops
                      in the Hadron Phase?
Kolb and Heinz(‟04)




                                                   Is v2(pT) really sensitive
                                                   to the late dynamics?




                                                                                  T.H. and K.Tsuda (‟02)
                                                         100MeV




                                                                  140MeV

                       0   0.2   0.4     0.6 0.8    0   0.2 0.4 0.6   0.8   1.0
                                       transverse momentum (GeV/c)
     Mean pT is the Key
                                                  Generic
                                                  feature!


 t                          t
Slope of v2(pT) ~ v2/<pT>
                                Response to decreasing Tth
                                (or increasing t)
                                      v2   <pT>    v2/<pT>
                                CE
                                PCE
 t
                            TH et al.(’05-)

(CGC +)QGP Hydro+Hadronic Cascade
          t              Hadronic
                         Corona
                         (Cascade,
                         JAM)
                         sQGP core
                         (Full 3D
                     z
                         Ideal Hydro)
              0          (Option)
                         Color Glass
                         Condensate
  Ideal QGP Fluid
  + Dissipative Hadron Gas Models
   hydro (1+1)D with              (2+1)D with         Full (3+1)D
          Bjorken flow            Bjorken flow
cascade
UrQMD     A.Dumitru et al.,
          PLB460,411(1999);
                                                      C.Nonaka and S.Bass,
                                                      nucl-th/0510038.
          PRC60,021902(1999);
          S.Bass and A.Dumitru,         N/A
          PRC61,064909(2000).

RQMD                              D.Teaney et al.,
                                  PRL86,4783(2001),

                 N/A              nucl-th/0110037;
                                  D.Teaney,                  N/A
                                  nucl-th/0204023.

JAM                                                   TH, U.Heinz,
                                                      D.Kharzeev, R.Lacey,
                 N/A                    N/A           and Y.Nara,
                                                      PLB636,299(2006).
                TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)

Hydro Meets Data for the First Time at
RHIC: “Current” Three Pillars
   1. Perfect Fluid (s)QGP Core
      • Ideal hydro description of the QGP phase
      • Necessary to gain integrated v2
   2. Dissipative Hadronic Corona
      • Boltzmann description of the hadron phase
      • Necessary to gain enough radial flow
      • Necessary to fix particle ratio dynamically
   3. Glauber Type Initial Condition
      • Diffuseness of initial geometry

   A Lack of each pillar leads to discrepancy!
  pT Spectra for identified hadrons
  from QGP Hydro+Hadronic Cascade




 dN/dy and dN/dpT are o.k. by hydro+cascade.
Caveat: Other components such as recombination and
fragmentation should appear in the intermediate-high pT regions.
Discussions: Hadronic Dissipation
• Hybrid Model:
QGP Fluid + Hadronic Gas + Glauber I.C.
                                ComparisonTry to draw
• Hydro Model:                  information on hadron gas

QGP Fluid + Hadronic Fluid + Glauber I.C.
Key technique in hydro:
•Partial chemical equilibrium in hadron phase
•Particle ratio fixed at Tch
Chemical equilibrium changes dynamics.
                TH and K.Tsuda(’02),TH and M.Gyulassy(’06)
Hadronic Dissipation Suppresses
Differential Elliptic Flow
                                      Difference comes
                                      from dissipation only
                                      in the hadron phase

                                  •Relevant parameter: Gs/t
                                                   Teaney(’03)
                                  •Dissipative effect is not so
                                  large due to small expansion
                                  rate (1/tau ~ 0.05-0.1 fm-1)


 Caveat: Chemically frozen hadronic fluid is essential in
 differential elliptic flow. (TH and M.Gyulassy (’06))

				
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posted:12/26/2011
language:English
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