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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 - PowerPoint PPT Presentation
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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