# Presentation: 506062

## Hydrodynamic Approach:Open Issues

**Tetsufumi Hirano**
**Special thanks to**
**Nu Xu, Miklos Gyulassy and Denes Molnar**

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

## Before Discussion

- Hydrodynamics is the heart of
- dynamical model in H.I.C.

- Some of the open questions are highly
- related with “Two particle correlation”
- and “thermal model”.

- sQGP
- HYDRO
- lQCD

- cQCD

- thermalization

- Hadron Spectra
- Fragmentation
- ReCo
- Cascade (hydro)

- jet

- pQCD

- lepton, photon

## 5. Summary

- Open our mind *!* Hydrodynamics can be used even for “high pT physics in HIC”.
- Jet tomography
- EM probe
- (J/ suppression)
- ...

- Keep in mind *!*
-    How robust is the current agreement of hydro?:
- Chemical non-eq.?
- Initial fluctuation?
- Viscosity?
- Thermalization?
- EoS?
- (Freeze-out?)

**Hydrodynamics is one of the**
** ****valuable tools at RHIC energies**

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

## Open 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 + cascade

## Lessons from My Talk on May 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 v2

**Rapidity Dependence of v****2**

_**Dimension**_
**Full 3D** **(***********s***** coordinate)**
_**EoS**_
- QGP + hadrons (chem. eq.)
**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.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 Approach

- 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 cascade

- Cooper-Frye formula (1972)

- 

- Out going particle flux

- In 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?

- Flow

- d

## Open Issues in Hadronic Cascade(with a help by D.Molnar)

*r*

- This instant interaction leads to acausal propagation
- especially in high particle density.
- How (un)realistic the viscous effects from hadronic
- cascade?
- 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

## Example

- Oversampling factor : N  N
- Cross section :   

-   infinity  Local

## Open 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 Check!

**Consistency Check!**

- Hydro

- Blast Wave
- Recombination
- Jet quenching
- CGC
- etc.

- feedback?

- information

## Vr vs. Tth

**V****r**** vs. T****th**

- T.H. and K.Tsuda (’02)

- Hydro: Au+Au at sqrt(sNN) = 130 GeV
- tau0 = 0.6fm/*c*

- ReCo(Duke)
- 200GeV

*T**c*

- Single F.O.
- by Broniowski
- & Florkowski
- 130GeV

- Blast Wave
- by Burward-Hoy
- 130GeV

- Az Blast Wave
- by Lisa & Retiere

- (175,0.55)

## <Vr> @ 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 Deconfinement Signal?

- R.Fries et al.(2003)

- Multi-strangeness sector may directly probe partonic
- collective flow. However, (*T*,*v*T)=(175,0.55) is gigantic!
- Accidental? Do we need another mechanism?
- UrQMD gives mass ordering and approximate scaling
- elliptic flow. (Hydro+jet model also does.)
- Blast wave  next slide

## Blast Wave Fit for ?

- Hydro
- (PCE)
- central

- What is important is interpretation after fitting.

## Approximate Hydro Line

- T.H. and M.Gyulassy

- B.W.model

## How to Get Large Radiiwithout Spoiling Single Spectra?

- Blast Wave Model
- (M.Lisa & F.Retiere)

- Rin ~11 fm
- Rout~12 fm

- J.Cramer & G.Miller
-    R~13fm

- T.H. and K.Tsuda(’02)

- Partial
- Chemical Eq.

- Hadronic afterburner helps?

- Tth and  are consistent
- with hydro. But...

## Initial Transverse Flow

- Hubble constant H = 0.25/fm

- Chojnacki et al.(2005)

## Initial Transverse Flow and Spectra

- 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 hydro+cascade approach is important...

- A revisit HBT radii from hydro
- How large the effect of resonance decays
- on 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 be
- nice to check it!

## Source fn.? Hydro?

- Tomasik & Wiedemann, hep-ph/0210250, page 31

- Source function: Resonance effects negligible
- Hydro: Increase HBT radii (Schlei et al.(1996))

- ???????

## HBT puzzle

## Results from Hydro at SPS

- 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 AMPT

- Lin, Ko, Pal(2002)

- Source is non-Gaussian.
- Positive x-t correlation
- Not only  decay,
-     but also “thermal” 

- Xout

- Xside

- Hydro
- (Kolb&Heinz)

- 30

- tau
- (fm/c)

- Completely different source shape/size

## Parton Density from Two Different Models

- I.Vitev, nucl-th/0404052

- Input: *R*AA
- Output:

- T.H. and Y.Nara (’04)

- Input: *dN*ch*/d***
- Output:

- 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 *n*g and *n*q

- (*N*f=3), (*N*f=2)

- >

- <

## Hydro + Rate Eq. in QGP phase

**Including gg********qqbar and gg********ggg**

**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 DescriptionBased 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 problem
- to be solved near future?
- What is the outstanding problem?
- What is missing?

## Toward a Unified Model (near future?)

- Proper time

- Transverse momentum

**CGC**
**(a la KLN)**

**Color Quantum**
**Fluid****(Q****S****2****<k****T****2****<Q****S****4****/********2****)**
**(*****x*****-evolution eq.)**

**Shattering CGC**
**(k****T**** factorization)**

**Hydrodynamics**
**(full 3D hydro)**

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

**Hadronic**
**cascade**
**(JAM)**

**Low p****T**

**High p****T**

**Recombination**

**Collinear factorized**
**Parton distribution**
**(CTEQ)**

**LOpQCD**
**(PYTHIA)**

- Nuclear wave
- function
- Parton distribution

- Parton
- production
- (dissipative
- process?)

- QGP

- Hadron
- gas

**Fragmentation**

**Freezeout**
**(chemical & thermal)**

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

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

**Jet quenching**

**Intermediate p****T**

- important in forward region?

- T.H. and Y.Nara (’02-)

## Thermalization/Isotropization?

- How does one connect CGC with sQGP?

- Gluons produced from
- two CGC collisions (KLN)

*E*T/*N *~ 1.6 GeV

- Initial condition
- of hydrodynamic
- simulations

*E*T/*N *~ 1.0 GeV

*E*T/*N *~ 0.55 GeV

-  Consistent with
- classical Yang Mills
- on 2D lattice (KNV)

-  Consistent with
- exp. data ~0.6 GeV

- Final (psuedo)rapidity
- spectra of all hadrons

- This should be obtained through
-  non-equilibrium processes.
-  Production of entropy

- Hydrodynamic evolution
- “*PdV* work” reduces *E*T/*N*.

## How “Perfect” is the sQGP?

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

- Dynamics of viscous fluids need to be solved

- T.H. and M.Gyulassy

## Dynamics of Viscous Fluids

- Relativistic Navier-Stokes
- is notorious equation
- in the sense that it violates
- causality.

- Introducing
- relaxation terms
- by hand
- (Teaney)

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

## Break Down of Naive Navier-Stokes Eq. and a Relaxation 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 QM2004

## Beyond Navier Stokes:“Extended Thermodynamics”

- How obtain additional equations?

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

- Balance eqs.

- Constitutive
- eqs.

- Muronga, Rischke, Chaudhuri, Heinz

## Open Source of Hydro?

- Practical, but important
-  issue in this field

## Open Source?

- AZHYDRO Ver.0.0
- (2+1) D hydro
- Author: P.Kolb
- BJ_HYDRO Ver.1.1
- (1+1)D hydro
- Author:A.Dumitru,
- D.H.Rischke

- Do you still want to use simple hydro
- model in spite of “NO-GO theorem”?
- Nevertheless, you want to try?
- If so, I will make our 3D hydro open to public.

**Notes:**
As far as I know, nobody uses these hydro models.
Does hydrodynamics itself have a power to constrain EOS?
It’s premature to do so.
It’s still the time to develop the model...
Nevertheless, someone wants to use 3D hydro. In that case, I can provide a code.
Some PHENIX and BRAHMS guys already have our code. But I never have their responses.

## Everybody thinks like this:Full 3D hydro with jet + CGC?It must be tough!

- 3D hydro+jet

- CGC+3D hydro

- T.H. and Y.Nara (’02-)

## http://quark.phy.bnl.gov/~hirano

- /hydrodata/par_evo.html

## “Hydro Lite” model (unofficial name)--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!!!

- HYDRO

- MODEL

## Functions

_**Current version:**_
- getrho(tau,x,y,eta): Local parton density
- gettemp(tau,x,y,eta): Local temperature
- getvx(tau,x,y,eta): Local vx
- getvy(tau,x,y,eta): Local vy

_**Next version:**_
- getInitialPosition(b,tau0,x,y,eta0):
-    Initial parton position with binary collision
- getInitialPosition(p0,phi0):
-    Initial parton momentum with power law tail
- getglv1st(tau,x,y,eta,p0): GLV 1st order
- getglv1sts(tau,x,y,eta,p0):
-    GLV 1st order neglecting kinematics
- moliere(p0): Elastic scattering angle
- opacityela(p0,opa): Elastic scattering angle at chi

## Example