S C O T T

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P R A T
H Y R O D Y N A M I C S
E X T E N D I N G
S C O T T
P U ZZ L E
M I C H I G A N
A N D
U N I V R S I T Y
T H
B T
S T T E
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OUTLINE

• Remnants of the HBT Puzzle
• Extending Hydrodynamics
• Tsunamis

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HBT Basics
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Blast-Wave Models
R
vzz/?
VxV?(r/R)
Parameters T, R, V? , ?, ??
Schnedermann, Sollfrank and Heinz Tomasik,
Broniowski, Lisa and Retiere,
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NA49 vs. Therminator
3-dimensional details of blast-wave confirmed
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Blast-Wave and the HBT Puzzle

• Parameters
• T ? 110 MeV
• R ? 13 fm
• V? ? 0.7c
• ? 10 fm/c
• ?? ? 3 fm/c

Requires Kp spectra
Rapid expansionsudden disintegration
Similar Conclusions Blast Waves (Lisa-Retiere,
Tomasik) Therminator Buda-Lund
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HYDRO
Overall sizes depend on EoS breakup criteria
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Cascade/Boltzmann
More resonances -gt softer -gt bigger Strings -gt
softer -gt bigger
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HBT and the EoS Dynamical Signature
Leads to Rout/Rside gtgt 1
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HBT and EoS Entropy
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HBT and EoSEntropy
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Is Lattice Eq. of State excluded?
Subrata Pal and S.P., PLB 2004
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Total Entropy and the lattice EOS

• Final S consistent with lattice EOS (Crude)
• Entropy moved from pions to baryons

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The HBT puzzle

• Rside/Rout?1 and ???10 fm/c suggest rapid
  expansion -gt hard EoS
• Entropy suggests softer EoS

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Explanations to the HBT Puzzle

• Refraction (Cramer-Miller, 2005)- Requires
  extreme assumptions
• Surface Emission (Heiselberg, 2002)- What
  happened to energy in center?
• Initial transverse velocity (Sinyukov, 2007)-
  Cause ???
• Super-Cooling (CsorgoCsernai, hep-th/9312230)

Needed Explanation with consistent dynamical
model
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Extending Hydrodynamics

1. Longitudinal Acceleration
2. Later times (Chemistry)
3. Earlier times (Shear)
4. In between (Hadronization dynamics)

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No Longitudinal Acceleration
Bjorken
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Analytic 1-D Solution(S.P. PRC 2007)
Bjorken
Accelerationless models underestimate lifetime
by ?10
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Later Times(Non-Equilibrium Chemistry Below Tc)

• Too many particles
• Pion, kaon, baryon fugacities gt 1
• Smaller P/?
• Less collective energy, more thermal

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Early Times (Shear)
In rest frame
Always true
Perfect Hydro Viscous Hydro
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Navier-Stokes
Bulk
Shear

• at early times
• Boosts early acceleration (D.Teaney,)
• Increases collective energy vs. thermal energy

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Early times

• For ?s/4?, Tzz becomes negative for ??0.6 fm/c
• Eq.s of Motions for Tij
• Saturate Anisotropy

saturatesanisotropy
relaxation time (Israel-Stewart)
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Anisotropy at early times
Collisionless Boltzmann
Classical Longitudinal Fields
CGC (Krasnitz, Nara Venugopalan)
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Intermediate Times(Bulk Viscosity in Mixed
Region)
K.Paech and S.P., PRC 2006
P
e
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Sigma Field out of Equilibrium
Langevin "force"
?? can blow up at phase transition!
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Example Linear Sigma Model
K.Paech A.Dumitru, PLB 623, 200 (2005)
1st order when ggt3.55
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Example Linear Sigma Model
For g3.4, Txx -gt 0
For big effects Should solve Sigma Eq.s of
Motion
K.Paech A.Dumitru, PLB 623, 200 (2005)
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How might this affect dynamics?
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Tsunamis at RHIC
See also nuclear doughnuts(Bauer and Bertsch,
PRL '90)
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Modeling Tsunamis at RHIC with Hydrodynamics
P
Resonance Gas
L
e
H
e
Increasing L or decreasing c2mixed -gt stronger
tsunami
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HydrodynamicEvolutionL2 GeV/fm3,c2mixed0.05
?1,3,5,7,9,11 fm/c
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Changing EoS
Large Rsidefor L?2 GeV/fm3
Bulk Viscosity in mixed phase strengthenstsunami
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Summary Slide 1
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Summary 2

• HBT is only hope to disentagle
• EoS
• Early-Time Shear
• Bulk Viscosity near Tc