HBT puzzle: from an ideal hydrodynamic point of view

1
HBT puzzle from an ideal hydrodynamic point of
view

• Tetsufumi Hirano

RHIC/AGS users meeting, BNL, NY, June 21, 2005
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Outline

• The sQGP core and the dissipative hadronic corona
  picture
• T.H. and M.Gyulassy,
  nucl-th/0506049
• How good/bad is the agreement of ideal hydro
  results with HBT data?
• Summary

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(No Transcript)
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Not Only the sQGP But Also
nucl-th/0506049
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Differential Elliptic Flow is the Key
p
p
elliptic flow
PHENIX white paper, nucl-ex/0410003
pT spectra
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Modeling of Hadron Phase and Freezeout
CLASS 3 Teaney, Lauret Shuryak Bass Dumitru
CLASS 1 Kolb, Sollfrank, Huovinen
Heinz Hirano
CLASS 2 Hirano Tsuda Teaney Kolb Rapp
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
No-Go theorem for class 1? see our paper!
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Cancel between v2 and ltpTgtin chemical eq. hadron
phase
v2(pT)
Chemical Eq.
v2(pT)
v2
Tth t
v2
ltpTgt
pT
v2(pT)
Chemical F.O.
ltpTgt
pT
Increase of ltpTgt with t is unrealistic from
particle ratio point of view!
v2
ltpTgt
pT
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Check Sheet for Prevailing Opinion
1. Ideal hydrodynamics reproduce v2(pT)
remarkably well, but not HBT radii.
TRUE FALSE
X
TRUE Ideal Hydrodynamics reproduces neither
v2(pT) nor HBT radii at RHIC.
2. v2(pT) is not sensitive to the late hadronic
stage.
TRUE FALSE
X
TRUE v2(pT) depends on thermal equilibrium,
chemical equilibrium, and viscous effects in the
hadron phase.
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Nearly Perfect Fluid of sQGP Core and the
Dissipative Hadronic Corona
T.H. and M.Gyulassy (05)

• Absolute value of viscosity

• Its ratio to entropy density

!
What makes this sudden behavior?
Nearly perfect fluidity of the sQGP AND imperfect
fluidity of hadrons are manifestation of
deconfinement!?
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How good/bad is the agreement of ideal hydro
results with HBT data?
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Rside, Rout, Rlong from Ideal Hydro
SIDE
OUT
CE Chemical Eq. PCE Partial Chem.Eq.
No resonance decays
LONG
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Lörstad and Sinyukov(1991)
Contour(Tconst.)
T(t) at origin
Model CE
proper time t (fm/c)
Model PCE
ltvrgt(Tth)
T.H. and K.Tsuda(02)
radius x (fm)
t
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AzHBT Radii
OUT
SIDE
STAR, PRC71, 044906(2005).
LONG
OUT-SIDE
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Npart1/3 scaling?
LINE AuAu200GeV PLOT AuAu62.4GeV
LINE AuAu200GeV PLOT CuCu200GeV
For dN/dh and v2 in CuCu collisions, see,
T.Hirano et al.,nucl-th/0506058
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Dilemma between Rside and Rlong
SIDE
LONG
Rside(KT0) 6fm (data) 4fm
(hydro)
Source size may grow by resonances (w mesons?).
Resonance decays also enhance Rlong!
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Resonances Enhance HBT Radii
Hydro(sQGP) RQMD(hadron) (D.Teaney)
See also, Soff, Bass, Dumitru HydroUrQMD
Steal from S.Pratts talk at RIKEN BNL
workshop(03)
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How to Get Large Radiiwithout Spoiling Single
Spectra?
Blast Wave Model (M.Lisa F.Retiere)
T.H. and K.Tsuda(02)
Partial Chemical Eq.
Tth and b are consistent with hydro. But
proper time t (fm/c)
Rin-plane 11 fm Rout-of-plane12 fm
J.Cramer G.Miller R12fm
radius (fm)
Hydro cannot get such a gigantic source radius!
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Vr vs. Tth
ReCo(Duke) 200GeV
Az Blast Wave by Lisa Retiere
(175,0.55)
Single F.O. by Broniowski Florkowski 130GeV
T.H. and K.Tsuda (02)
Hydro AuAu at sqrt(sNN) 130 GeV tau0 0.6fm/c
Tc
Blast Wave by Burward-Hoy 130GeV
Note F.O. parameter ? A set of Tth, b, AND S.
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Initial Transverse Flow
Hubble constant H 0.25/fm
Chojnacki et al.(2005)
Positive correlation Hubble-like flow
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Initial Transverse Flow and Spectra
Initial flow a.la. Kolb and Rapp(02)
p
H 0.02/fm ltlt 0.25/fm
K
T.H. (05)
Dissipation in hadron phase also makes
pT spectrum hard. (Teaney(02)) ?No room for
initial flow!?
p
CAVEAT total energy 2(collision energy) for
H0.25/fm
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Initial Flow Effect on HBT Radii
OUT
SIDE
Hubble const. Rout, Rlong
Rout/Rside 1 for H0.25 fm-1
LONG
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Temperature Distribution at t6.0 fm/c
H0.02/fm
H0.25/fm
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Summary

• The HBT puzzle is still puzzling us (only me?)!
• Fitting the HBT radii is NOT the solution of the
  puzzle. Justify parameters after fitting spectra
  and HBT radii ! Especially, dynamical aspects
  such as radial flow, source size etc.
• Dissipative hadronic corona is important to
  reproduce elliptic flow. However, HBT radii
  cannot be reproduce by the hybrid model yet.

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Fitting Parameters by CramerMiller
J.G.Cramer et al.,PRL94,102302(2005)
Proton pT slope can be reproduced?
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Pion Chemical Potential
Partial chemical equilibrium (PCE)
(T,mp) (173,123)
T.H. and K.Tsuda(02)
t
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BONUS SLIDES!
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Basis of the Announcement
PHENIX white paper
NA49(03)
Integrated elliptic flow
Differential elliptic flow
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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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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
Models for Hadron Phase v2(pT,m) pT spectra Yield or ratio Viscous effect Caveat
Chemical Equilibrium Yes Yes No No P (Pbar) yields ltlt exp. data
Partial Chemical Equilibrium No Yes Yes No Only low pT for pions
Hadronic Cascade Yes Yes Yes Yes Kinetic approach Boundary (QGP??hadron)
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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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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
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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!