Dynamical Modeling of Dynamical Modeling of Relativistic Heavy Ion Relativistic Heavy Ion

CollisionsCollisionsTetsufumi Hirano

Workshop at RCNP, Nov 4, 2004

Work in partly collaboration withY.Nara (Frankfurt), M.Gyulassy (Columbia)

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

The Five Pillars of RHIC WisdomThe Five Pillars of RHIC WisdomIdeal hydro

Quark recombination constituent q d.o.f.

CGC

Statistical model

Early thermalization + soft EOS

Very high inferred initial gluon density

Very high anticipated initial gluon density

u, d, s equil-ibration near Tcrit

Slide from T.HallmanTalk@ICHEP04~STAR white paper

The State of RHIC TheoryThe State of RHIC Theory

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

Statisticalmodel:

equilib’n or phase space?

Hydro: 0, freezeout,

boost-invariance

ambigs.

Quark recomb.: predictive

power?Parton E loss:

untested assump-

tions

Gluon saturation: universal

scale estab-lished?

Emerging description of beautiful evolution from one

new state of matter to another!

AndYet,

A patchwork, with model parameters adjusted independ-

ently for each element

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

estimates of theoretical uncertainties

Slide from T.HallmanTalk@ICHEP04~STAR white paper

Hairsplitting Comments from Our Approach

How are these consistent with each other?

Discussion from hydrodynamic point of view:1. Hydro vs. Statistical model (main topic)2. Hydro vs. Recombination model3. Hydro vs. Jet tomography4. Hydro vs. CGC

These discussions will tell us what to do nextand lead to a unified understanding of HIC.

Today’s Bad NewsToday’s Bad News

The elliptic flow at RHIC is

“accidentally”reproduced by a hydro model.

Hydro vs. Statistical Model (1)

Chemical parameters particle ratioThermal parameters pt spectra

•Statistical modelTch>Tth

•(conventional) hydroTch=Tth

• No reproductionof ratio and spectrasimultaneously

Hydro vs. Statistical Model (2)

P.Huovinen, QM2002 proceedings

Hydro vs. Statistical Model (3)

iIntroduction of chemical potentialfor each hadron!

•Single Tf in hydro•Hydro works?•Both ratio andspectra?

Hydro vs. Statistical Model (4)

EOS

Example of chem. potential

Partial chemical equilibrium (PCE)

Expansion dynamics is changed(or not)?

T.H

. an

d K

.Tsu

da(

’02)

Hydro vs. Statistical Model (5)

Model PCE

Model CE

Contour(T=const.)

T() at origin

T.H

. an

d K

.Tsu

da(

’02)

<vr>(Tth)

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 chemicallyfrozen hydro

• No way to fix Tth

• Suggests necessity of (semi)hard components

Charged hadronsin AuAu 130GeV

Hydro vs. Statistical Model (7)

ChemicalEquilibrium

PartialChemical

Equilibrium

K

p

T.H. and K.Tsuda (’02)

Ko

lb a

nd

Hei

nz(

’04)

Is v2(pT) sensitive to the late dynamics?

Hydro vs. Statistical Model (8)

Slope of v2(pT) ~ v2/<pT> Response to decreasing Tth

(or increasing )v2 <pT> v2/<pT>

CE

PCE

Genericfeature!

pdV work + (number)/(entropy)

Hydro vs. Statistical Model (9) Simplest case: Pion gas

Longitudinal expansion pdV work!

dET/dy should decrease with decreasing Tth. <ET>dN/dy should so.

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.

Hydro vs. Statistical Model (10)

PHENIX white paper, nucl-ex/0410003

Hydro vs. Statistical Model (11)

•Choice of Tth in conventional hydro results fromneglecting chemical f.o.•The great cost one has to pay for “simplification”!• Importance of chemical potential for each hadronswithin 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 NewsToday’s Good NewsCurrently,

hydro+cascade is the only modelwhich reproduces

the elliptic flow, particle ratio, andparticle spectra.

Caveat: Need realistic interface andoversampling to get rid of numericalartifacts.

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

Hydro vs. Recombination (1)

R.J

.Fri

es

et a

l. (’

03)

Tc=175MeV & vT = 0.55???

reco(Duke)

T.H

. and K.T

suda (’02)

Half of radial flow comes from hadron phase in hydro

Parameter dependence?

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

Hydro vs. Recombination (2) Soft+hard reco is

important?Naïve idea:Hydro+jet modelwith recombinationvia string fragmentation

PHENIX “modelkiller” plot!nucl-ex/0408007 Pick

up apartonfromQGP

Only mass effect

T.H

.,QM

200

4

Associated yield1.7<pT<2.5GeV/c

Hydro vs. Jet Tomography (1)

I.Vite

v, n

ucl

-th

/04

040

52

Input: RAA

Output:

T.H

. an

d Y.N

ara (’0

4)

Input: dNch/dOutput:

consistent?

Hydro vs. Jet Tomography (2)Jet tomography:

“Color charge density”Hydrodynamics:Parton density

cf.) Parton density in chem. eq.

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

rate eq. for ng and nq

(Nf=3), (Nf=2)

>

<

Hydro vs. CGC (1)K

har

zeev

an

d L

evi

n (

’01

)

Gluons produced fromtwo CGC collisions (KLN)

ET/N ~ 1.6 GeVConsistent with classical Yang Mills on 2D lattice (KNV, Lappi)Inconsistent with exp. data ~0.6GeV

T.H

. an

d Y.N

ara(’0

4)

Hydro vs. CGC (2)Gluons produced fromtwo CGC collisions (KLN)

ET/N ~ 1.6 GeV

Initial conditionof hydrodynamicsimulations

ET/N ~ 1.0 GeV ET/N ~ 0.55 GeV Consistent withclassical Yang Millson 2D lattice (KNV)

Consistent withexp. data ~0.6 GeV

Final (psuedo)rapidityspectra of all hadrons

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:1.“The right model in the right place” basis

• Time scale• Energy/momentum scale

2.Consistency among models3.Treatment of interface among models4.The number of parameters/assumptions as small as possible