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A N OUTLINE What does HBT Measure? Models HBT and the Equation of State Dynamical Signatures Entropy Tsunamis, EoS & Viscosity Scott Pratt The HBT Puzzle and the RHIC Tsunami
What does HBT measure? Determines Shape of f(p,r,t) Scott Pratt The HBT Puzzle and the RHIC Tsunami HBT Basics Rlong Rside Rout R side + v Scott Pratt
The HBT Puzzle and the RHIC Tsunami 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
The HBT Puzzle and the RHIC Tsunami Blast Wave Fits QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. Lisa and Retiere, PRC 70:044907 (04) Therminator Broniowski et al., nucl-th/0212053
Scott Pratt The HBT Puzzle and the RHIC Tsunami NA49 vs. Therminator 3-dimensional details of blast-wave confirmed Scott Pratt The HBT Puzzle and the RHIC Tsunami 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 expansion sudden disintegration Similar Conclusions: Blast Waves (Lisa-Retiere, Tomasik) Therminator Buda Lund Scott Pratt The HBT Puzzle and the RHIC Tsunami HYDRO
Overall sizes depend on EOS & breakup criteria Scott Pratt The HBT Puzzle and the RHIC Tsunami Cascade/Boltzmann More resonances -> softer -> bigger Strings -> softer -> bigger Scott Pratt The HBT Puzzle and the RHIC Tsunami HBT and the EoS: Dynamical Signature
Leads to: Rout/Rside >> 1 Scott Pratt The HBT Puzzle and the RHIC Tsunami HBT and EoS: Entropy Sizes and spectra give phase space density rr 2 3 d r[ f( p, r)] r f ( p) rr 3
d r f( p, r) p 3/2 dN / d 3 p = (2 S + 1) Rou Rlong Rside Phase space density gives Entropy dS dN 5 3 1 2p pdp E 3 ln(2)ln[ f( p )] 3/2 f( p ) dy d p 2 2 2
Scott Pratt The HBT Puzzle and the RHIC Tsunami HBT and EoS: Entropy increases with s1/2 gives entropy for pions Rinv and spectra for other species gives total S Scott Pratt The HBT Puzzle and the RHIC Tsunami Is Lattice Eq. of State excluded?
Range Scott Pratt The HBT Puzzle and the RHIC Tsunami Total Entropy and the lattice EOS Final S consistent with lattice EOS CRUDE! Entropy moved from pions to baryons Scott Pratt The HBT Puzzle and the RHIC Tsunami The HBT puzzle
Models that fit overall volume (fit entropy) underpredict Rside Scott Pratt The HBT Puzzle and the RHIC Tsunami 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 - Source ???
(Sinyukov, 2007) Needed: Explanation with consistent dynamical model Scott Pratt The HBT Puzzle and the RHIC Tsunami (Bauer and Bertsch, PRL '90) Tsunamis at RHIC Scott Pratt vwave = gh
The HBT Puzzle and the RHIC Tsunami P Modeling Tsunamis at RHIC with Hydrodynamics cs2 =dPde Resonanc e Gas eH cs2 =consan cs2 =0.3
L e Increasing L or decreasing c2mixed -> stronger tsunami Scott Pratt The HBT Puzzle and the RHIC Tsunami Hydrodynamic Evolution L=2 GeV/fm3, c2mixed=0.05 =1,3,5,7,9,11 fm/c Scott Pratt The HBT Puzzle and the RHIC Tsunami
HBT Radii 2 cmixed =0.05 2 cmixed =0.15 Large Rside for L2 GeV/fm3 Scott Pratt The HBT Puzzle and the RHIC Tsunami
Viscosity and Tsunamis: Perfect Hydro: Txx =Tyy =Tzz = P Navier-Stokes: Tzz = P h(2zvz x vx yvy) Bgv Israel-Stewart: Scott Pratt t Tij = (1 / )(Tij TijN .S. ) The HBT Puzzle and the RHIC Tsunami Initial-State Asymmetry
of Tij Relativistic Gas: Txx =Tyy =Tzz =e / 3 Classical Longitudinal Fields: CGC (Krasnitz, Nara &Venugopalan) : Txx =Tyy =e Tzz =e Txx =Tyy e / 2
Tzz 0 For =0.5 fm/c -> Significant strengthening of tsunami Scott Pratt The HBT Puzzle and the RHIC Tsunami Non-Zero Shear Even for h s/4p -> significant strengthening of tsunami Scott Pratt The HBT Puzzle and the RHIC Tsunami
K.Paech and S.P., PRC 2006 Bulk Viscosity in Mixed Region P P Bgv e -> Significant strengthening of tsunami Scott Pratt The HBT Puzzle and the RHIC Tsunami Summary HBT invaluable for investigating EoS: - HBT + spectra -> entropy
Large experimental Rside might indicate tsunami - Driven by Softness in EoS and viscosity More serious analysis is needed Scott Pratt The HBT Puzzle and the RHIC Tsunami