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A N D Scott Pratt P H R Y E X T E N A N D Scott Pratt P H R Y E X T E N D I N A S C O T T G R T O D P M Y U I N Z C U A Z H N M L I I I T H E G C V B T S S TA T E N R S I T Y Extending Hydrodynamics and the HBT Puzzle Michigan State University

OUTLINE • Remnants of the HBT Puzzle • Extending Hydrodynamics • Tsunamis Scott Pratt OUTLINE • Remnants of the HBT Puzzle • Extending Hydrodynamics • Tsunamis Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

HBT Basics Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HBT Basics Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Blast-Wave Models R vz=z/ Vx=V (r/R) Parameters: T, R, V , , Schnedermann, Sollfrank Blast-Wave Models R vz=z/ Vx=V (r/R) Parameters: T, R, V , , Schnedermann, Sollfrank and Heinz Tomasik, Broniowski, Lisa and Retiere, … Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

NA 49 vs. Therminator 3 -dimensional details of blast-wave confirmed Scott Pratt Extending Hydrodynamics NA 49 vs. Therminator 3 -dimensional details of blast-wave confirmed Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Blast-Wave and the HBT Puzzle Parameters: T 110 Me. V R 13 fm V Blast-Wave and the HBT Puzzle Parameters: T 110 Me. V R 13 fm V 0. 7 c 10 fm/c 3 fm/c Requires Kp spectra Rapid expansion sudden disintegration Similar Conclusions: Blast Waves (Lisa-Retiere, Tomasik) Therminator Buda-Lund Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

HYDRO Overall sizes depend on Eo. S & breakup criteria Scott Pratt Extending Hydrodynamics HYDRO Overall sizes depend on Eo. S & breakup criteria Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Cascade/Boltzmann More resonances -> softer -> bigger Strings -> softer -> bigger Scott Pratt Cascade/Boltzmann More resonances -> softer -> bigger Strings -> softer -> bigger Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

HBT and the Eo. S: Dynamical Signature Leads to: Rout/Rside >> 1 Scott Pratt HBT and the Eo. S: Dynamical Signature Leads to: Rout/Rside >> 1 Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

HBT and Eo. S: Entropy Sizes and spectra give phase space density Phase space HBT and Eo. S: Entropy Sizes and spectra give phase space density Phase space density gives Entropy Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

HBT and Eo. S: Entropy Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan HBT and Eo. S: Entropy Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Is Lattice Eq. of State excluded? Subrata Pal and S. P. , PLB 2004 Is Lattice Eq. of State excluded? Subrata Pal and S. P. , PLB 2004 Range Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Total Entropy and the lattice EOS • Final S consistent with lattice EOS (Crude) Total Entropy and the lattice EOS • Final S consistent with lattice EOS (Crude) • Entropy moved from pions to baryons Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

The HBT puzzle • Rside/Rout 1 and 10 fm/c suggest rapid expansion > hard The HBT puzzle • Rside/Rout 1 and 10 fm/c suggest rapid expansion > hard Eo. S • Entropy suggests softer Eo. S Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Explanations to the HBT Puzzle • Refraction (Cramer-Miller, 2005) - Requires extreme assumptions • 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 (Csorgo&Csernai, hep-th/9312230) Needed: Explanation with consistent dynamical model Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Extending Hydrodynamics 1. 2. 3. 4. Scott Pratt Longitudinal Acceleration Later times (Chemistry) Earlier Extending Hydrodynamics 1. 2. 3. 4. Scott Pratt Longitudinal Acceleration Later times (Chemistry) Earlier times (Shear) In between (Hadronization dynamics) Extending Hydrodynamics and the HBT Puzzle Michigan State University

No Longitudinal Acceleration Bjorken Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State No Longitudinal Acceleration Bjorken Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Analytic 1 -D Solution (S. P. PRC 2007) en rk Bjo Accelerationless models underestimate Analytic 1 -D Solution (S. P. PRC 2007) en rk Bjo Accelerationless models underestimate lifetime by 10% Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Later Times (Non-Equilibrium Chemistry Below T c) • Too many particles • Pion, kaon, Later Times (Non-Equilibrium Chemistry Below T c) • Too many particles • Pion, kaon, baryon fugacities > 1 • Smaller P/ • Less collective energy, more thermal Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Early Times (Shear) In rest frame: Always true Perfect Hydro: Viscous Hydro: Scott Pratt Early Times (Shear) In rest frame: Always true Perfect Hydro: Viscous Hydro: Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Navier-Stokes Bulk Shear • at early times • Boosts early acceleration (D. Teaney, ) Navier-Stokes Bulk Shear • at early times • Boosts early acceleration (D. Teaney, ) • Increases collective energy vs. thermal energy Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Early times • For =s/4 , Tzz becomes negative for 0. 6 fm/c • Early times • For =s/4 , Tzz becomes negative for 0. 6 fm/c • Eq. s of Motions for Tij • Saturate Anisotropy saturates anisotropy relaxation time (Israel-Stewart) Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Anisotropy at early times Collisionless Boltzmann: Classical Longitudinal Fields: CGC (Krasnitz, Nara &Venugopalan) : Anisotropy at early times Collisionless Boltzmann: Classical Longitudinal Fields: CGC (Krasnitz, Nara &Venugopalan) : Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

K. Paech and S. P. , PRC 2006 Intermediate Times (Bulk Viscosity in Mixed K. Paech and S. P. , PRC 2006 Intermediate Times (Bulk Viscosity in Mixed Region) P Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Sigma Field out of Equilibrium Langevin Sigma Field out of Equilibrium Langevin "force" can blow up at phase transition! Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

K. Paech & A. Dumitru, PLB 623, 200 (2005) Example: Linear Sigma Model 1 K. Paech & A. Dumitru, PLB 623, 200 (2005) Example: Linear Sigma Model 1 st order when g>3. 55 Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Example: Linear Sigma Model For g=3. 4, Txx -> 0 For big effects: Should Example: Linear Sigma Model For g=3. 4, Txx -> 0 For big effects: Should solve Sigma Eq. s of Motion K. Paech & A. Dumitru, PLB 623, 200 (2005) Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

P How might this affect dynamics? Txx r Scott Pratt Extending Hydrodynamics and the P How might this affect dynamics? Txx r Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

See also nuclear doughnuts Tsunamis at RHIC Scott Pratt (Bauer and Bertsch, PRL '90) See also nuclear doughnuts Tsunamis at RHIC Scott Pratt (Bauer and Bertsch, PRL '90) Extending Hydrodynamics and the HBT Puzzle Michigan State University

Modeling Tsunamis at RHIC with Hydrodynamics P Resonance Gas H L Increasing L or Modeling Tsunamis at RHIC with Hydrodynamics P Resonance Gas H L Increasing L or decreasing c 2 mixed -> stronger tsunami Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Hydrodynamic Evolution L=2 Ge. V/fm 3, c 2 mixed=0. 05 =1, 3, 5, 7, Hydrodynamic Evolution L=2 Ge. V/fm 3, c 2 mixed=0. 05 =1, 3, 5, 7, 9, 11 fm/c Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

Changing Eo. S Large Rside for L 2 Ge. V/fm 3 Bulk Viscosity in Changing Eo. S Large Rside for L 2 Ge. V/fm 3 Bulk Viscosity in mixed phase strengthens tsunami Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University

? Extending Hydrodynamics and the HBT Puzzle Boltzmann Dynamic Fields Dynamic Tij Scott Pratt ? Extending Hydrodynamics and the HBT Puzzle Boltzmann Dynamic Fields Dynamic Tij Scott Pratt Navier-Stokes Summar y Slide #1 Michigan State University

Summary #2 HBT is only hope to disentagle • Eo. S • Early-Time Shear Summary #2 HBT is only hope to disentagle • Eo. S • Early-Time Shear • Bulk Viscosity near Tc Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University