What did we learn from v2pT m at RHIC

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What did we learn fromv2(pT m) at RHIC?

• Tetsufumi Hirano and Miklos Gyulassy

The Berkeley School, LBNL, CA, May 19, 2005
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(No Transcript)
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Basis of the Announcement
PHENIX white paper
NA49(03)
Integrated elliptic flow
Differential elliptic flow
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Are Hydro Results Consistentwith Each Other?
What does it mean?

• Purposes of this talk
• To clarify the origin of difference among hydro
  results
• To claim the importance of viscous effects in
  the hadron phase
• (Dissipative Hadronic Corona)

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
T
1 fm/c
QGP phase
Ideal hydrodynamics
Tc
3 fm/c
Partial Chemical Equilibrium EOS
Chemical Equilibrium EOS
Tch
Hadronic Cascade
Hadron phase
Tth
Tth
10-15 fm/c
t
Sudden freezeout l0?infinity
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TthltTch

• Statistical model
• TchgtTth
• (conventional) hydro
• TchTth

• No reproduction
• of ratio and spectra
• simultaneously

Chemical parameters ? particle ratio Thermal
parameters ? pt spectra
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Many people dont know this
P.Huovinen, QM2002 proceedings
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Extension of Parameter Space

• Single Tf in hydro
• Hydro works?
• Both ratio and
• spectra?

Introduction of chemical potential for each
hadron!
mi
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Chemical Potential EoS
EOS
Partial chemical equilibrium (PCE)
Example of chem. potential
T.H. and K.Tsuda(02)
Expansion dynamics is changed (or not)?
t
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Does Dynamics change?
Contour(Tconst.)
T(t) at origin
Model CE
ltvrgt(Tth)
Model PCE
T.H. and K.Tsuda(02)
t
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pT Spectra

• How to fix Tth in conventional hydro
• Response to pT slope
• Spectrum harder with decreasing Tth
• Up to how large pT?

Chemical Equilibrium
T.H. and K.Tsuda (02)
Partial Chemical Equilibrium

• Tth independence of slope in chemically frozen
  hydro
• No way to fix Tth
• Suggests necessity of
• (semi)hard components

Charged hadrons in AuAu 130AGeV
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Elliptic Flow
Kolb and Heinz(04)
Is v2(pT) really sensitive to the late dynamics?
100MeV
T.H. and K.Tsuda (02)
140MeV
0.8
1.0
0.4
0.6
0.2
0
0.8
0.4
0.6
0.2
0
transverse momentum (GeV/c)
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Mean pT is the Key
Generic feature!
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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Cancel between v2 and ltpTgt
v2(pT)
Chemical Eq.
v2(pT)
v2
Tth t
v2
ltpTgt
pT
v2(pT)
Chemical F.O.
ltpTgt
pT
v2
ltpTgt
pT
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Why ltpTgt behaves differently?
Simplest case Pion gas
Longitudinal expansion ? pdV work!
dET/dy
ideal hydro
proper time

• CFO dS/dy const.
• dN/dy const.
• ltpTgt MUST 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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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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Summary of Results
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Summary

• What have we learned?
• From hydrocascade analyses, viscosity is
  mandatory in the hadron phase QGP as a perfect
  fluid and hadrons as a viscous fluid.
• 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).
• Comment
• Conventional (chem. equilibrium ideal) hydro
  makes full use of neglecting chemical f.o. to
  reproduce v2(pT) and pT spectra. Accidental
  reproduction!

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Fuzzy image if focus is not adjusted yet.
focus hadron corona
QGP
Wanna see this?
QGP
QGP
Fine-tune the hadronic focus!
The importance of the dissipative hadronic corona
to understand perfect fluid sQGP core!
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BONUS SLIDES!
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Finite Mean Free Path Viscosity
See, e.g. DanielewiczGyulassy(1985)
For ultra-relativistic particles, the shear
viscosity is
Ideal hydro l ? 0 ? shear viscosity ? 0
Transport cross section
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FAQ

• We cannot say Hydro works very well at RHIC
• anymore?

• Yes/No. Only a hydrocascade model does a good
  job.
• Nevertheless, HBT puzzle!
• QGP as a perfect fluid. Hadron as a viscous fluid.

2. Why ideal hydro can be used for chemically
frozen hydro?

• We can show from
• AND .
• One has to distinguish chemical freeze out
• from chemical non-equilibrium.

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Todays Breaking News
May 19 2005
The Berkeley Tribune
Ideal hydrodynamics with chemical equilibrium
accidentally reproduces transverse
momentum dependence of the elliptic flow at RHIC.
(T.H.)
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Large radial flow reduces v2 for protons
Blast wave peak depends on f
High pT protons
x
y
pT

• Radial flow pushes protons to high pT regions
• Low pT protons are likely to come from fluid
  elements with small radial flow

Low pT protons
Even for positive elliptic flow of matter, v2
for heavy particles can be negative in low pT
regions!
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v2(pT) Stalls in Hadron Phase?
Hadronic rescattering via RQMD does not change
v2(pT) for p !

• Mechanism for stalling v2(pT)
• Hydro (chem. eq.)
• Cancellation between
• v2 and ltpTgt
• ?Effect of EoS
• HydroRQMD
• Effective viscosity
• ?Effect of finite l

D.Teaney(02)
PbPb, SPS 17 GeV, b6 fm
Solid lines are guide to eyes