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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

Hairsplitting Comments from Our Approach

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.

Hydro vs. Statistical Model (1)

- Statistical model

Tch>Tth

- (conventional) hydro

Tch=Tth

- No reproduction

of ratio and spectra

simultaneously

Chemical parameters particle ratio

Thermal parameters pt spectra

Hydro vs. Statistical Model (2)

P.Huovinen, QM2002 proceedings

Hydro vs. Statistical Model (3)

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

spectra?

Introduction of chemical potential

for each hadron!

mi

Hydro vs. Statistical Model (4)

EOS

Partial chemical equilibrium (PCE)

Example of chem. potential

T.H. and K.Tsuda(’02)

Expansion dynamics is changed

(or not)?

t

Hydro vs. Statistical Model (5)

Contour(T=const.)

T(t) at origin

Model CE

<vr>(Tth)

Model PCE

T.H. and K.Tsuda(’02)

t

Hydro vs. Statistical Model (6)

- 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

Hydro vs. Statistical Model (7)

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)

Hydro vs. Statistical Model (8)

Generic

feature!

pdV work + (number)

/(entropy)

t

t

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

Response todecreasing Tth

(or increasing t)

t

Hydro vs. Statistical Model (9)

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.

Hydro vs. Statistical Model (10)

PHENIX white paper, nucl-ex/0410003

Hydro vs. Statistical Model (11)

- 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?

Today’s Good News

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.

Hydro vs. Recombination (1)

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?

Hydro vs. Recombination (2)

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

Hydro vs. Jet Tomography (1)

T.H. and Y.Nara (’04)

I.Vitev, nucl-th/0404052

Input: dNch/dh

Output:

Input: RAA

Output:

consistent?

Hydro vs. Jet Tomography (2)

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

Hydro vs. CGC (1)

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

Hydro vs. CGC (2)

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.

Hydro vs. CGC (3)

- 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?

Summary so far

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

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