3-D Hydro: present and future

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3-D Hydropresent and future

• Tetsufumi Hirano
• Columbia University

Second RHIC II Science Workshop _at_ BNL, Probes of
EOS
2
Outline

• Warming up
• Current Results from ideal hydro
• Proposal No.1
• Revisit of v2(pT)
• Proposal No.2
• Summary

3
Why 3-D Hydro?
If one wants to analyze
PHOBOS, nucl-ex/0407012
BRAHMS, PRL88,202301(2002)
or
within hydro, one needs a 3-D hydro since one can
assume neither the Bjorken solution nor
cylindrical symmetry.
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Warming Up No. 1No Boost Invariant Region at
RHIC?

• Basic assumption
• Finite Bjorken rod (-h0lthslth0)
• Massless pions
• Thermal distribution

R
2h0
Space-time rapidity
Folding Local thermal distributions with the box
profile, you get Gaussian-like momentum dist.
For details, see Schnedermann, PRC48,2462(93).
Boost inv. region at RHIC is not ruled out! Dont
mix up hs with y!
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Warming Up No.2 v2(h) and v2(y)
Jacobian as an weight fn.
P. Kolb, Heavy Ion Phys.15, 279(2002).
dN/dh or dN/dy
v2
10 effect
Jacobian between y and h
Example from 3D hydro
v2(h) has a peak even in boost inv. solution.
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Results from Ideal Hydro
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Particle Density Dependence of v2
NA49(03)
Kolb, Sollfrank, Heinz (00)

• Dimension
• 2Dboost inv.
• EoS
• QGP hadrons (chem. eq.)
• Decoupling
• Sudden freezeout

(response)(output)/(input)

• Hydrodynamic response is
• const. v2/e 0.2 _at_ RHIC
• Exp. data reach hydrodynamic
• limit at RHIC for the first time.

Number density per unit transverse area
Dawn of the hydro age!
Hydro picture only in central collisions???
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pT Dependence of v2
T.H.(04)

• Dimension
• Full 3D (t-hs coordinate)
• EoS
• QGP hadrons (chem. frozen)
• Decoupling
• Sudden freezeout

high pT
(response)(output)/(input)
low pT
b11fm

• Low pT ? Hydrodynamic scaling
• High pT ?Deviation from hydro scaling.

particle density
low
high
Forward region?
spatial anisotropy
large
small
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Rapidity Dependence of v2

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

T.H. and K.Tsuda(02)

• Dimension
• Full 3D (t-hs coordinate)
• EoS
• QGP hadrons (chem. eq.)
• QGP hadrons (chem. frozen)
• Decoupling
• Sudden freezeout

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v2/e as a function h
T.H.(05)

• Dimension
• Full 3D (t-hs coordinate)
• EoS
• QGP hadrons (chem. frozen)
• Decoupling
• Sudden freezeout
• No resonance decay

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/e(h)? Yes ?
Forward region Midrapidity with the
same particle density No ? Nontrivial dynamics
in forward region
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Proposal 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?

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Revisit of v2(pT)
T.H. and M.Gyulassy (05)
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(No Transcript)
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Are Hydro Results Consistentwith Each Other?
What does it mean?
p
p
elliptic flow
PHENIX white paper, nucl-ex/0410003
pT spectra
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Modeling of Hadron Phase and Freezeout
Hirano Tsuda Teaney Kolb Rapp
Teaney, Lauret Shuryak Bass Dumitru
Kolb, Sollfrank, Huovinen Heinz Hirano
Ideal hydrodynamics
QGP phase
Tc
Partial Chemical Equilibrium EOS
Chemical Equilibrium EOS
Tch
Hadronic Cascade
Hadron phase
Tth
Tth
t
Sudden freezeout l0?infinity
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v2(pT) depends on Tth
Partial Chemical Equilibrium
Chemical Equilibrium
p
140MeV
Kolb and Heinz(04)
100MeV
K
p
Is v2(pT) really sensitive to the late dynamics?
T.H. and K.Tsuda (02)
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Mean pT is the Key
Generic feature! See next slide!
t
t
Slope of v2(pT) v2/ltpTgt
Response to decreasing Tth (or increasing t)
v2
v2/ltpTgt
ltpTgt
CE
PCE
t
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dET/dy and n/s
Simplest case Pion gas
Longitudinal expansion ? pdV work!
dET/dy
ideal hydro
proper time

• CFO dS/dy const.
• dN/dy const.
• ltpTgt decreases
• CE dS/dy const.
• dN/dy decreases (mass effect)
• ltpTgt can increase as long as ltETgtdN/dy decreases.

dET/dy should decrease with decreasing Tth. ?
ltETgtdN/dy should so.
Result from the 1st law of thermodynamics
Bjorken flow
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Comments

• 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 (ltpTgt) 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!

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Can v2 at Forward Rapidity be Reproduced by Hydro
Cascade ?
Teaney, Lauret, Shuryak(01)

• Dimension
• 2Dboost inv.
• EoS
• Parametrized by latent heat
• (LH8, LH16, LH-infinity)
• Hadrons
• QGPhadrons (chem. eq.)
• Decoupling
• Hybrid (Boltzmann eq.)

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

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Summary for Revisit of v2(pT)
A hydro cascade model by Teaney et al. is the
only dynamical model to reproduce v2 and v2(pT)
properly.
Viscous effect is mandatory in the hadron phase
The announcement should have been QGP as a
perfect fluid, hadrons as a viscous fluid !?
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Proposal No.2

• Need a new hydro cascade model in full 3D (t,
  h, x, y) coordinate
• Full 3D hydro in t-h 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, (11)D hydro UrQMD
• Teaney, Lauret Shuryak (21)D hydro RQMD
• We desperately need people to do the above study.

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Summary

• Bulk dynamics in forward region
• Hydro scaling (and its violation?)
• v2/e(h) or v2/e(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.

Support Our Phenomenologist!
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Blast Wave Fit in Forward Region
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).
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Centrality Dependence of e
CGC works well for centrality dependence of
multiplicity.
eCGCgt epart, ecoll
v2 is 20-25 larger than the others.
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Fuzzy image if focus is not adjusted yet.
focus hadron gas
QGP
Wanna see this?
QGP
QGP
fine tuning of focus!