Refractive%20Distortions%20to%20HBT%20A%20Classical%20View

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Refractive Distortions to HBTA Classical View
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OUTLINE

• Theory background
• Classical description of refractive distortion
• Examples
• Classical vs. QuantumCramer et al.,Miller,
  PRL94, 102302 (05),Miller and Cramer,
  nucl-th/0507004H.W.Barz, PRC59, 2214 (99)
  PRC53, 2536 (96)

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What can correlations measure?
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What is puzzling about HBT

• Several simple models work
• Blast wave parametersR13 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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Adding Mean Field

• Classical Method
• Calculate trajectories
• Weight with 1 cos(pa-pb)(xa-xb)

• Quantum Method
• Sample last-collision points
• Weight with ?(pa,xa)2?(pb,xb)2
  ??(pa,xa)?(pb,xa)??(pa,xb)?(pb,xb)

Outgoing wave functions
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Classical Ilustration of Refraction
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Louisville Theorem and Refraction

• Escaping attractive mean field lowers
  (contracts) p
• Contraction of p space -gt expansion of x space

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Simple Analytic Example
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Simple Analytic Model
Stronger distortions for larger range
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Simple Model with Collective Flow

• Classical trajectories begin at R
• Thermal T120, yM0.8
• Longitudinal boost invariance
• Let mean field exp-(r-R)/a
• R moves outward with rapidity (?9 fm/c, R9fm,
  yB 0.4) (?12 fm/c, R12fm, yB 0) (?15
  fm/c, R9fm, yB -0.4)
• Surface consumes returning trajectories

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Simple Model with Collective Flow

• Rside more distorted than Rlong
• Stronger distortions in expanding phase

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Quantum vs. Classical
r0
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Quantum
Classical
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Quantum vs. Classical
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Quantum vs. Classical Eikonal Phases
Kapusta and Li, www.arXiv.org0505075 C.Y. Wong,
J.Phys G30, S1053 (04) arXivhep-ph/0403025 M.
Chu et al., PRC50, 3079 (94)
Interference phase
Use vdE/dp assume pa-pb is small
Classical asymptotic separation
time delay
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Summary

• Refraction can be important
• Attractive forces help interpretation of Rside
• Any attractive interaction should help (pisobar)
• Classical treatments (Boltzmann) work