a52e396b71e1231adba03838e76222a0.ppt
- Количество слайдов: 34
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 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 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 and the HBT Puzzle Michigan State University
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 and the HBT Puzzle Michigan State University
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 Extending Hydrodynamics and the HBT Puzzle Michigan State University
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 State University
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) • 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 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 • 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 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 University
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, 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 Extending Hydrodynamics and the HBT Puzzle Michigan State University
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 • 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) : Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University
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 "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 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 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 HBT Puzzle Michigan State University
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 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, 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 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 Navier-Stokes Summar y Slide #1 Michigan State University
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


