3-D Hydro:3-D Hydro:present and futurepresent and future

Tetsufumi HiranoTetsufumi Hirano

Columbia UniversityColumbia University

Second RHIC II Science Workshop @ BNL, Probes of EOS

OutlineOutline

• Warming up• Current Results from ideal hydro• Proposal No.1

• Revisit of v2(pT)

• Proposal No.2• Summary

Why 3-D Hydro?Why 3-D Hydro?If one wants to analyze

PHOBOS, nucl-ex/0407012

or

BRAHMS, PRL88,202301(2002)

within hydro, one needs a 3-D hydrosince one can assume neither

the Bjorken solution nor cylindrical symmetry.

Warming Up No. 1Warming Up No. 1No Boost Invariant Region at RHIC?No Boost Invariant Region at RHIC?

Basic assumptionBasic assumption1. Finite “Bjorken rod” (-0<s<0)2. Massless pions3. Thermal distribution

20

Spac

e-tim

e ra

pidi

ty

Boost inv. region at RHIC is not ruled out!Boost inv. region at RHIC is not ruled out!Don’t mix up Don’t mix up ss with y! with y!

R

Folding Local thermal distributionswith the box profile, you getGaussian-like momentum dist.

For details, see Schnedermann, PRC48,2462(’93).

Warming Up No.2: vWarming Up No.2: v22(() and ) and vv22(y)(y)

P. Kolb, Heavy Ion Phys.15, 279(2002).Jacobian as an weight fn.Jacobian as an weight fn.

Jacobian between Jacobian between yy and and Example from 3D hydroExample from 3D hydro

v2() has a peak even in boost inv. solution.

~10% effect

v2dN/dor dN/dy

Results fromResults fromIdeal HydroIdeal Hydro

Particle Density Particle Density Dependence of vDependence of v22

•Hydrodynamic response isconst. v2/ ~ 0.2 @ RHIC•Exp. data reach hydrodynamiclimit at RHIC for the first time.

(re

spo

nse

)=(o

utp

ut)/

(inp

ut)

Number density per unit transverse area

• Dimension• 2D+boost inv.

• EoS• QGP + hadrons (chem.

eq.)• Decoupling

• Sudden freezeout

NA49(’03) Kolb, Sollfrank, Heinz (’00)

Dawn of the hydro age!Dawn of the hydro age!

Hydro picture only in central collisions???

““ppTT” Dependence of v” Dependence of v22

“high pT”

“low pT”

• Dimension• Full 3D (s coordinate)

• EoS• QGP + hadrons (chem.

frozen)• Decoupling

• Sudden freezeout

T.H.(’04)

particledensity lowhigh

spatialanisotropy

largesmall

•Low pT “Hydrodynamic scaling”•High pT Deviation from hydro scaling.

(re

spo

nse

)=(o

utp

ut)/

(inp

ut)

Forward region?

b~11fm

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)

vv22// as a function as a function

• Dimension• Full 3D (s coordinate)

• EoS• QGP + hadrons (chem.

frozen)• Decoupling

• Sudden freezeout• No resonance decay

T.H.(’05)

Caveat 1: v2 can be reduced by increasing Tth in forward region.Caveat 2: Eccentricity can depend on rapidity.

Is the hydro scaling seen in v2/()?Yes Forward region ~ Midrapidity with the same particle density No Nontrivial dynamics in forward region

Proposal No.1Proposal No.1• Can hydro scaling be seen in forward

rapidity AND low pT regions?

• Need to measure pT of particles in forward rapidity.

• Doable within current detector?– FTPC at STAR?– Forward Spectrometer at BRAHMS?– PHENIX/PHOBOS?

• Need detector upgrade/high luminosity?

Revisit of vRevisit of v22(p(pTT))T.H. and M.Gyulassy (’05)

Are Hydro Results Consistentwith Each Other? What does it

mean?

PH

EN

IX w

hite

pa

per, nu

cl-ex/0

41

000

3

elliptic flow

pT spectra

p

Modeling of Hadron Phase and Modeling of Hadron Phase and FreezeoutFreezeout

Tc

QG

P p

has

eH

ad

r on

ph a

s e

Partial

Chemical

Equilibrium

EOS

Hirano & Tsuda;Teaney;

Kolb & Rapp

Teaney, Lauret & Shuryak;

Bass & Dumitru

Tch

Tth

Hadronic

Cascade

Chemical

Equilibrium

EOS

Tth

Kolb, Sollfrank,Huovinen & Heinz;

Hirano;…

Ideal hydrodynamics

Sudden freezeout: =0infinity

vv22(p(pTT) depends on T) depends on Tthth

ChemicalEquilibrium

PartialChemical

Equilibrium

K

p

T.H. and K.Tsuda (’02)

Ko

lb a

nd

Hei

nz(

’04)

Is v2(pT) really sensitiveto the late dynamics?

100MeV

140MeV

Mean pT is the Key

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

(or increasing )v2

PCE

CE

v2/<pT><pT>

Generic Generic feature!feature!

See See next next slide!slide!

dET/dy and n/s Simplest case: Pion gasLongitudinal 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.

Result from the 1st law of thermodynamics &

Bjorken flow

dET/d

y

proper time

ideal hydro

CommentsComments

• v2 is sensitive to the early stage of collisions, whereas v2(pT) can also be sensitive to the late stage since v2(pT) is manifestation of interplay between radial flow (<pT>) and elliptic flow (v2).

• Conventional (chem. equilibrium & ideal) hydro makes full use of neglecting chemical f.o. (particle ratios) to reproduce v2(pT) and pT spectra. Accidental reproduction!

Can vCan v22 at Forward Rapidity at Forward Rapidity be Reproduced by Hydro + be Reproduced by Hydro +

Cascade ?Cascade ?• Dimension

• 2D+boost inv.• EoS

• Parametrized by latent heat (LH8, LH16, LH-infinity)• Hadrons• QGP+hadrons (chem. eq.)

• Decoupling• Hybrid (Boltzmann eq.)

Teaney, Lauret, Shuryak(’01)

• Deviation at lower energies can be filled by “viscosity” in hadron gases• Latent heat ~0.8 GeV/fm3 is favored.

A hydro + cascade model by Teaney et al. is the only dynamical

model to reproduce v2 and v2(pT) properly.

“Viscous” effect is mandatoryin the hadron phase

The announcement should havebeen “QGP as a perfect fluid,hadrons as a viscous fluid” !?

Summary for Revisit of Summary for Revisit of vv22(p(pTT))

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.

Support Our Phenomenologist!Support Our Phenomenologist!

SummarySummary• Bulk dynamics in forward region

– Hydro scaling (and its violation?)

– v2/() or v2/(b) in forward and low pT region.

• To understand the QGP, we need the transport of hadrons.

3D hydro + hadron cascade• We cannot learn anything from data

without dynamical analyses.

R.Debbie (BRAHMS), proceeding for The 8th Conference on Intersections of R.Debbie (BRAHMS), proceeding for The 8th Conference on Intersections of Particle And Nuclear Physics (CIPANP2003), New York City, New York (May 19-24, 2003).Particle And Nuclear Physics (CIPANP2003), New York City, New York (May 19-24, 2003).

Blast Wave Fit in Forward Blast Wave Fit in Forward RegionRegion

Centrality Dependence of Centrality Dependence of

CGC> part, coll

v2 is 20-25% largerthan the others.

CGC works well for centrality dependence of multiplicity.

QGPQGP

Fuzzy imageif focus is not adjusted yet.

QGPQGPQGP Wanna see this?

“fine tuning” of focus!focus:

hadron gas