I S

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H B T
P U Z Z L I N G ?
I S
R E A L L Y
S T A T E
M I C H I G A N
P R A T T
S C O T T
U N I V E R S I Y
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PUZZLES
What do the measurements tell us?

• Theory
• Blast wave

• Why is the breakup density so high?
• Have we excluded the lattice EOS?
• How does it expand so fast and
  dissolve so suddenly?

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All the theory you need to know
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Blast Wave
R
vzz/?
VxV?(r/R)
Parameters T, R, V? , ?, ??
Schnedermann, Sollfrank and Heinz Tomasik,
Broniowski, Lisa and Retiere,
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Blast-Wave Fits
Lisa and Retiere, PRC 70044907 (04)
Broniowski et al.,nucl-th/0212053
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Blast-Wave Fits

• Parameters
• T ? 110 MeV
• R ? 13 fm
• V? ? 0.7c
• ? 10 fm/c (or less)
• ?? ? 3 fm/c (or less)

Requires Kp spectra
Rapid expansionsudden disintegration
Similar Conclusions Blast Waves (Lisa-Retiere,
Tomasik) Therminator Buda Lund
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Are the sizes too small?
Breakup densities are high
Adamova et al, PRL90 022301 (03)

• Hadronic cascades give similar sizes!!!
• Matter is expanding
• Density is falling
• Expansion becoming Hubble-like Chojnacki et
  al, PRC71 044902 (04)

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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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Is lattice Eq. of State excluded?

• Entropy
• determined by initial ? and EOS
• conserved

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Is lattice Eq. of State excluded?

• ltfgt increases with s1/2
• gives entropy for pions
• Rinv and spectra for other species gives total S

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Is Lattice Eq. of State excluded?
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Total Entropy and the lattice EOS

• Final S consistent with lattice EOS
• CRUDE!
• Entropy moved from pions to baryons
• Chemical rates are important

Greiner,GongMueller, PLB316226-230(93) PrattHag
lin, PRC593304-3308(99) RappShuryak,
PRL.862980-2983(01)
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How does it expand dissolve so fast?

• Blast wave parameters R13 fm, ?10 fm/c,
  v0.7c
• Surface grows 7 fm in 10 fm/c
• What about acceleration?
• Reducing Rside or increasing ? would help

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How does it expand dissolve so fast?

• Reduced Emissivity
• Non-infinite longitudinal extent
• Longitudinal acceleration
• Shear Viscosity
• Refraction of the mean field

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1. Reduced Emissivity
Sequential emission
Hubble-like expansion

• Reasons for lower emissivity
• phase change
• super-cooling CsorgoCsernai, hep-th/9312230

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2. Non-infinite longitudinal extent
Assume boost invariance -gt underestimate ?
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3. Longitudinal Acceleration
Let surface (endcap) accelerate from y0 to yf

• Ignore longitudinal a -gt underestimate ?
• 3D codes are better Csorgo,Grassi,Hama,Kodama
  , PLB565, 107 (03) Hirano, nucl-th/040017

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4. Shear Viscosity
Shear viscosity increased transverse
acceleration Teaney, nucl-th/0403053 Longitudinal
classical fields -gt hyper-viscous
Note Viscosity kills v2 Cheng etal, PRC65024901
(02)
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Refraction of the mean field
Cramer et al.,Miller, PRL94, 102302 (05),Miller
and Cramer, nucl-th/0507004H.W.Barz, PRC59, 2214
(99) PRC53, 2536 (96) Kapusta and Li,
www.arXiv.org0505075 C.Y. Wong,
hep-ph/0403025 M. Chu et al., PRC50, 3079 (94)
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Refraction of the mean field

• Stronger for low pt
• Stronger for Rside

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How does it expand and dissolve so fast?

• All 5 corrections -gt longer ? or smaller Rside
• Improved modeling required