Hydrodynamic Approach:Hydrodynamic Approach:Open IssuesOpen Issues

Tetsufumi HiranoSpecial thanks to

Nu Xu, Miklos Gyulassy and Denes Molnar

The Berkeley School, LBNL, CA, May 27, 2005

Before DiscussionBefore DiscussionHydrodynamics is the heart of

dynamical model in H.I.C.

Some of the open questions are highlyrelated with “Two particle correlation”

and “thermal model”.

sQGPHYDRO

lQCDcQCD

thermalization

Hadron Spectra•Fragmentation•ReCo•Cascade (hydro)

jetpQCD

lepton, photon

5. Summary5. Summary

• Open our mind Open our mind !! Hydrodynamics Hydrodynamics can be used even can be used even for “high pfor “high pTT physics in HIC”.physics in HIC”.– Jet tomographyJet tomography– EM probeEM probe– (J/(J/ suppression) suppression)– ……

• Keep in mind Keep in mind !! How robust is the How robust is the

current agreement current agreement of hydro?:of hydro?:– Chemical non-eq.?Chemical non-eq.?– Initial fluctuation?Initial fluctuation?– Viscosity?Viscosity?– Thermalization?Thermalization?– EoS?EoS?– (Freeze-out?)(Freeze-out?)

Hydrodynamics is one of the valuable tools at RHIC energies

T.H., “Hydrodynamic Models”, talk at QM2004T.H., “Hydrodynamic Models”, talk at QM2004

Open IssuesOpen Issues• Open Issues in hydro + cascade models

– Hybrid approach helps to understand v2(eta)?– Boundary? Transport Properties?

• How well the hydrodynamics works? Check the consistency (ReCo, B.W., etc.) Feedback from other approaches? (Large source

radius, chemical composition, etc.) Still need to check resonance effects on HBT? A “unified” dynamical approach based on hydro?

(How large viscous effects?)• How can one profit from hydro?

Open source? “Hydro-Lite” model (Easy way to check consistensy)

Full 3D hydro + cascadeFull 3D hydro + cascade

Lessons from My Talk on Lessons from My Talk on May 19May 19

• Dissipative hadronic corona of the “perfect fluid” sQGP core is important.

• Ideal hydro description for hadronic matter is ruled out! (You should refer to Teaney’s results from now!)

• One should pay attention to accidental reproduction of data a little bit more! Bold assumptions sometimes cause a big mistake! As many data as possible within one dynamical approach.

Rapidity Dependence of vRapidity Dependence of v22

• Dimension• Full 3D (s coordinate)

• EoS1. QGP + hadrons (chem. eq.)2. QGP + hadrons (chem. frozen)

• Decoupling• Sudden freezeout

•Low density Deviation from hydro•Forward rapidity at RHIC~ Midrapidity at SPS? Heinz and Kolb (’04)

T.H. and K.Tsuda(’02)

Proposal No.2Proposal No.2• Need a new hydro + cascade model in

full 3D (x, y) coordinate– Full 3D hydro in - coordinate

• T.H. or SPheRIO group (Brazil)– Combine hydro with one of the hadronic cascade

models (Self proposal?!)

– Extension of current hydro + cascade• Bass & Dumitru, (1+1)D hydro + UrQMD• Teaney, Lauret & Shuryak, (2+1)D hydro +

RQMD

• We desperately need people to do the above study.

T.H., talk at RHIC II Science Workshop (probe of EOS session) Apr.29

Caveats for a Hybrid Caveats for a Hybrid ApproachApproach

• Caveat1: Boundary btw. hydro and cascade (comment by Bugaev)

• Caveat2: How reliable viscosity is in hadronic cascade? (comments by Molnar, (Pratt), Gyulassy)

Both Problems need quantitative discussion

Boundary btw. hydro and Boundary btw. hydro and cascadecascade

Cooper-Frye formula (1972)

Out going particle fluxIn coming particle flux

To obey the energy momentum conservation,in-coming flux is mandatory.

Obviously, it depends on flow profile.How large at RHIC? How does dynamics change?

Flowd

Open Issues in Hadronic Open Issues in Hadronic CascadeCascade

(with a help by D.Molnar)(with a help by D.Molnar)

r

This instant interaction leads to acausal propagationespecially in high particle density.How (un)realistic the viscous effects from hadroniccascade?

The scheme might introduce unwanted viscous effect.Does hydro+cascade make full use of “artificial”viscosity to get excellent agreement with data?

Cheng et al(2002)

r: Interaction range

ExampleExampleOversampling factor : N NCross section :

infinity Local

Open IssuesOpen Issues• Open Issues in hydro + cascade models

– Hybrid approach helps to understand v2(eta)?– Boundary? Transport Properties?

• How well the hydrodynamics works? Check the consistency (ReCo, B.W., etc.) Feedback from other approaches? (Large source

radius, chemical composition, etc.) Still need to check resonance effects on HBT? A “unified” dynamical approach based on hydro?

(How large viscous effects?)• How can one profit from hydro?

Open source? “Hydro-Lite” model (Easy way to check consistensy)

Consistency Consistency Check!Check!

Blast WaveRecombinationJet quenchingCGCetc.

feedback?information

Vr vs. TthT

.H.

and

K.T

suda

(’0

2)

Hydro: Au+Au at sqrt(sNN) = 130 GeVtau0 = 0.6fm/c

ReCo(Duke)200GeV

Tc

Single F.O.by Broniowski& Florkowski130GeV

Blast Waveby Burward-Hoy130GeV

Az Blast Waveby Lisa & Retiere

(175,0.55)

<V<Vrr> @ Hadronization> @ Hadronization

Model: CGC+Hydro(+Jet) , T.H. and Y.Nara (2004)Impact parameter: b=2.4 fm (0-6% centrality)Initial parameters tuned to reproduce PHOBOS dN/deta with 0=0.6fm/c. No pre-thermal diffusion.

0 (fm/c) <vr>|||<0.5

0.1 0.30

1.0 0.27

3.0 0.18

The sQGP gives just <vr>=0.2-0.3!

ReCo Really Suggests ReCo Really Suggests Deconfinement Signal?Deconfinement Signal?

R.Fries et al.(2003)Multi-strangeness sector may directly probe partoniccollective flow. However, (T,vT)=(175,0.55) is gigantic!Accidental? Do we need another mechanism?UrQMD gives mass ordering and approximate scalingelliptic flow. (Hydro+jet model also does.)Blast wave next slide

Blast Wave Fit for Blast Wave Fit for ??Hydro(PCE)central

What is important is interpretation after fitting.

Approximate Hydro LineApproximate Hydro LineT.H. and M.Gyulassy

B.W.model

How to Get Large RadiiHow to Get Large Radiiwithout Spoiling Single without Spoiling Single

Spectra?Spectra?Blast Wave Model(M.Lisa & F.Retiere)

Rin ~11 fmRout~12 fm

J.Cramer & G.Miller R~13fm

T.H. and K.Tsuda(’02)

PartialChemical Eq.

Hadronic afterburner helps?

Tth and are consistentwith hydro. But…

Initial Transverse FlowInitial Transverse FlowHubble constant H = 0.25/fm Chojnacki et al.(2005)

Initial Transverse Flow and Initial Transverse Flow and SpectraSpectra

H = 0.02/fm << 0.25/fm

P.Kolb and R.Rapp(2002)

What is the origin?Isotherm f.o.?F.O. prescription?

Although I already told Although I already told hydro+cascade approach is hydro+cascade approach is

important…important…

A revisit HBT radii from hydroHow large the effect of resonance decayson HBT radii in hydro?Nobody checks at RHIC energies.Is it worth checking it?KK correlation?I don’t believe this directly solves the puzzle. However, it would benice to check it!

Source fn.? Hydro?Source fn.? Hydro?Tomasik & Wiedemann, hep-ph/0210250, page 31

Source function: Resonance effects negligibleHydro: Increase HBT radii (Schlei et al.(1996))

???????

HBT puzzleHBT puzzle

Results from Hydro at Results from Hydro at SPSSPS

Richard M. Weiner wrote: Dear Tetsufumi Hirano, I read with interest some of your papers and wonder whether in the mean time you have considered  the effect of resonances on HBT (in your paper nucl-th/0205043 you explicitly mention this fact). Our experience at SPS, cf. e.g. Weiner, Phys. Reports 327 (2000) 249-346, in particular page 319 tells me that consideration of resonances might solve the HBT "puzzle". Most recently Akkelin, Syniukov nucl-th/0310036 have reached the same conclusion.

HBT from AMPTHBT from AMPT

Lin, Ko, Pal(2002)

Source is non-Gaussian.Positive x-t correlationNot only decay, but also “thermal”

Xout

Xsi

deHydro(Kolb&Heinz)

30

tau(fm/c)

Completely different source shape/size

Parton Density from Two Different Models

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?

Chemical Composition of QGP?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 + Rate Eq. in QGP phase

Including ggqqbar and ggggg

Collision term:

T.S.Biro et al.,Phys.Rev.C48(’93)1275.

Assuming “multiplicative” fugacity, EoS is unchanged.

Jet Tomography Chemical Composition of sQGP

Unified DescriptionUnified DescriptionBased on HydroBased on Hydro

Is this the right approach in H.I.C.(I strongly believe the answer is YES.)If so, what is the first priority problemto be solved near future?What is the outstanding problem?What is missing?

Toward a Unified Model Toward a Unified Model (near future?)(near future?)

Pro

per

time

Transverse momentum

CGCCGC(a la KLN)(a la KLN)

Color QuantumColor QuantumFluidFluid(Q(QSS

22<k<kTT22<Q<QSS

44//22))((xx-evolution eq.)-evolution eq.)

Shattering CGCShattering CGC(k(kTT factorization) factorization)

HydrodynamicsHydrodynamics(full 3D hydro)(full 3D hydro)

Parton energy lossParton energy loss(a la Gyulassy-Levai-Vitev)(a la Gyulassy-Levai-Vitev)

HadronicHadroniccascadecascade(JAM)(JAM)

Low pLow pTT High pHigh pTT

RecombinationRecombination

Collinear factorizedCollinear factorizedParton distributionParton distribution(CTEQ)(CTEQ)

LOpQCDLOpQCD(PYTHIA)(PYTHIA)

Nuc

lear

wav

efu

nctio

nP

arto

n di

strib

utio

n

Par

ton

prod

uctio

n(d

issi

pativ

epr

oces

s?)

QG

PH

adro

nga

s

FragmentationFragmentationFreezeoutFreezeout(chemical & thermal)(chemical & thermal)

(MV model(MV modelon 2D lattice)on 2D lattice)

(classical Yang-Mills(classical Yang-Millson 2D lattice)on 2D lattice)

Jet quenchingJet quenching

Intermediate pIntermediate pTT

important in forward region?

T.H. and Y.Nara (’02-)

Thermalization/Thermalization/Isotropization?Isotropization?

How does one connect CGC with sQGP?

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.

How “Perfect” is the How “Perfect” is the sQGP?sQGP?

Reynolds number = (kinetic term)/(viscous term)

Dynamics of viscous fluids need to be solved

T.H

. and

M.G

yula

ssy

Dynamics of Viscous Dynamics of Viscous FluidsFluids

Relativistic Navier-Stokesis notorious equationin the sense that it violatescausality.

Introducing relaxation termsby hand(Teaney)

Solving equationsbeyond Navier-Stokes(Muronga & Rischke,Chaudhuri & Heinz)

Break Down of Naive Break Down of Naive Navier-Stokes Eq. and a Navier-Stokes Eq. and a Relaxation MethodRelaxation Method•Non-relativistic case (Based on discussion by Cattaneo (1948))

0: Fourier’s law

: “relaxation time”

Parabolic equation (heat equation)ACAUSAL!!

Finite Hyperbolic equation (telegraph equation)

Balance eq.:

Constitutive eq.:

T.H., “Hydrodynamic Models”, talk at QM2004T.H., “Hydrodynamic Models”, talk at QM2004

Beyond Navier Stokes:Beyond Navier Stokes:“Extended Thermodynamics”“Extended Thermodynamics”

How obtain additional equations?

In order to ensure the second law of thermodynamics , one can choose

Balance eqs.

Constitutiveeqs.

Muronga, Rischke, Chaudhuri, Heinz

Open Source of Hydro?Open Source of Hydro?

Practical, but important issue in this field

Open Source?Open Source?•AZHYDRO Ver.0.0 (2+1) D hydroAuthor: P.Kolb•BJ_HYDRO Ver.1.1 (1+1)D hydroAuthor:A.Dumitru,D.H.Rischke

Do you still want to use simple hydromodel in spite of “NO-GO theorem”?

Nevertheless, you want to try?If so, I will make our 3D hydro open to public.

Everybody thinks like this:Everybody thinks like this:Full 3D hydro with jet + Full 3D hydro with jet +

CGC?CGC?It must be tough!It must be tough!

3D hydro+jetCGC+3D hydro

T.H. and Y.Nara (’02-)

http://quark.phy.bnl.gov/~hirano/hydrodata/par_evo.html

““Hydro Lite” model Hydro Lite” model (unofficial name)(unofficial name)

--What you can utilize----What you can utilize--Solution of hydrodynamic simulations:

•Parton density•Temperature (>Tc)•transverse flow Safe to use hydro data T>Tc

@ (, x, y, s)

Applying suggestion:•Parton Energy Loss•Recombination•Thermal photon•All depend on your idea!!!

FunctionsFunctionsCurrent version:Current version:

getrho(tau,x,y,eta): Local parton densitygettemp(tau,x,y,eta): Local temperaturegetvx(tau,x,y,eta): Local vxgetvy(tau,x,y,eta): Local vy

Next version:Next version:getInitialPosition(b,tau0,x,y,eta0): Initial parton position with binary collisiongetInitialPosition(p0,phi0): Initial parton momentum with power law tailgetglv1st(tau,x,y,eta,p0): GLV 1st ordergetglv1sts(tau,x,y,eta,p0): GLV 1st order neglecting kinematicsmoliere(p0): Elastic scattering angleopacityela(p0,opa): Elastic scattering angle at chi

ExampleExample