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Dynamical Modeling of Relativistic Heavy Ion Collisions

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Dynamical Modeling of Relativistic Heavy Ion Collisions

Tetsufumi Hirano

Work in partly collaboration with

Y.Nara (Frankfurt), M.Gyulassy (Columbia)

Workshop at RCNP, Nov 4, 2004

The Five Pillars of RHIC Wisdom

Slide from T.Hallman

~STAR white paper

Ideal hydro

Early thermalization + soft EOS

Statistical model

Quark recombination constituent q d.o.f.

…suggest appealing QGP-based picture of RHIC collision evolu-tion, BUT invoke 5 distinct models, each with own ambigu-ities, to get there.

u, d, s equil-ibration near Tcrit

pQCD parton E loss

CGC

Very high inferred initial gluon density

Very high anticipated initial gluon density

Hydro: 0, freezeout, boost-invariance ambigs.

Statisticalmodel: equilib’n or phase space?

LQCD: CPU limitations; applic’y to dynamic matter?

Gluon saturation: universal scale estab-lished?

Quark recomb.: predictive power?

Parton E loss: untested assump-tions

Slide from T.Hallman

~STAR white paper

The State of RHIC Theory

A patchwork, with model parameters adjusted independ-ently for each element

Emerging description of beautiful evolution from one new state of matter to another!

And

Yet,

In order to rely on theory for compelling QGP discovery claim, we need:greater coherence; fewer adjusted parameters; quantitative estimates of theoretical uncertainties

How are these consistent with each other?

Discussion from hydrodynamic point of view:

- Hydro vs. Statistical model (main topic)
- Hydro vs. Recombination model
- Hydro vs. Jet tomography
- Hydro vs. CGC

These discussions will tell us what to do next

and lead to a unified understanding of HIC.

The elliptic flow

at RHIC is

“accidentally”

reproduced by

a hydro model.

- Statistical model
Tch>Tth

- (conventional) hydro
Tch=Tth

- No reproduction
of ratio and spectra

simultaneously

Chemical parameters particle ratio

Thermal parameters pt spectra

P.Huovinen, QM2002 proceedings

- Single Tf in hydro
- Hydro works?
- Both ratio and
spectra?

Introduction of chemical potential

for each hadron!

mi

EOS

Partial chemical equilibrium (PCE)

Example of chem. potential

T.H. and K.Tsuda(’02)

Expansion dynamics is changed

(or not)?

t

Contour(T=const.)

T(t) at origin

Model CE

<vr>(Tth)

Model PCE

T.H. and K.Tsuda(’02)

t

- How to fix Tth in conventional hydro
- Response to pT slope
- Spectrum harder as decrease Tth
- Up to how large pT?

- Tth independence of slope in chemically
frozen hydro

- No way to fix Tth
- Suggests necessity of
(semi)hard components

Charged hadrons

in AuAu 130GeV

Partial

Chemical

Equilibrium

Chemical

Equilibrium

p

Kolb and Heinz(’04)

K

p

Is v2(pT) sensitive to

the late dynamics?

T.H. and K.Tsuda (’02)

Generic

feature!

pdV work + (number)

/(entropy)

t

t

Slope of v2(pT) ~ v2/<pT>

Response todecreasing Tth

(or increasing t)

t

Simplest case: Pion gas

Longitudinal expansion

pdV work!

CFO: dS/dy = const.

- dN/dy = const.
- <pT> decreases
CE: dS/dy = const.

- dN/dy decreases (mass effect)
- <pT> can increase as long as <ET>dN/dy decreases.

dET/dy should decrease with

decreasing Tth.

<ET>dN/dy should so.

PHENIX white paper, nucl-ex/0410003

- Choice of Tth in conventional hydro results from
neglecting chemical f.o.

- The great cost one has to pay for “simplification”!
- Importance of chemical potential for each hadrons
within hydrodynamics

- “No-Go theorem”. Yet you use?
- >90% hydro results at SPS and RHIC do not
make sense!

- Chemical eq. mimics viscous hydro?

Currently,

hydro+cascade is the only model

which reproduces

the elliptic flow, particle ratio, and

particle spectra.

D.Teaney et al., nucl-th/0110037.

Caveat: Need realistic interfaceand

oversampling to get rid of numerical

artifacts.

Today, I won’t discuss (violation of) energy conservation,

decrease of entropy…

reco(Duke)

R.J.Fries et al. (’03)

T.H. and K.Tsuda (’02)

Half of radial flow comes from hadron phase in hydro

Tc=175MeV & vT = 0.55???

Parameter dependence?

Soft+hard reco is

important?

Naïve idea:

Hydro+jet model

with recombination

via string fragmentation

Only mass

effect

T.H.,QM2004

PHENIX “model

killer” plot!

nucl-ex/0408007

Pick

up a

parton

from

QGP

Associated yield

1.7<pT<2.5GeV/c

T.H. and Y.Nara (’04)

I.Vitev, nucl-th/0404052

Input: dNch/dh

Output:

Input: RAA

Output:

consistent?

Hydrodynamics:

Parton density

Jet tomography:

“Color charge density”

cf.) Parton density in chem. eq.

(Nf=3), (Nf=2)

>

<

Not complete chem. eq.! Need chemical non-eq. description

rate eq. for ng and nq

Gluons produced from

two CGC collisions (KLN)

Kharzeev and Levin (’01)

T.H. and Y.Nara(’04)

ET/N ~ 1.6 GeV

- Consistent with classical Yang Mills on 2D lattice (KNV, Lappi)
- Inconsistent with exp. data ~0.6GeV

Initial condition

of hydrodynamic

simulations

Gluons produced from

two CGC collisions (KLN)

Final (psuedo)rapidity

spectra of all hadrons

ET/N ~ 1.6 GeV

ET/N ~ 1.0 GeV

ET/N ~ 0.55 GeV

Consistent with

classical Yang Mills

on 2D lattice (KNV)

Consistent with

exp. data ~0.6 GeV

This should be obtained through

non-equilibrium processes.

Production of entropy

Hydrodynamic evolution

“PdV work” reduces ET/N.

- Need a mechanism to reduce ET/N ?
- ET and/or N
- Non-equilibrium description is extremely important.
- Can we get a short thermalization
time (~1fm/c)?

- Is Boltzmann (elastic+inelastic) sufficient
for this?

- If not, may we need non-eq. quantum field
approaches?

- Can we get a short thermalization

We should keep in mind in modeling of HIC:

- “The right model in the right place” basis
- Time scale
- Energy/momentum scale

- Consistency among models
- Treatment of interface among models
- The number of parameters/assumptions
as small as possible