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Why 3-D Hydro? If one wants to analyze PHOBOS, nucl-ex/ or BRAHMS, PRL88,202301(2002) within hydro, one needs a 3-D hydro since one can assume neither the Bjorken solution nor cylindrical symmetry.
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3-D Hydro:3-D Hydro:present and futurepresent and future
Tetsufumi HiranoTetsufumi HiranoColumbia 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 rap
idity
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
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.
(res
pons
e)=(
outp
ut)/(
inpu
t)
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.
(res
pons
e)=(
outp
ut)/(
inpu
t)
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?
Are Hydro Results Consistentwith Each Other? What does it
mean?
PH
EN
IX w
hite paper, nucl-ex/0410003
elliptic flow
pT spectra
p
Modeling of Hadron Phase and Modeling of Hadron Phase and FreezeoutFreezeout
Tc
QG
P p
hase
Had
ron
phas
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)
Kol
b an
d H
einz
(’04)
Is v2(pT) really sensitiveto the late dynamics?
100MeV140MeV
Mean pT is the Key
Slope of v2(pT) ~ v2/<pT> Response to decreasing Tth
(or increasing )v2
PCE
CEv2/<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.