s c o t t prattpratt m i c h i g a n statestate u n i v e r s i y t s u n a m i thethe b t...

S C O T T

PRATT

M I C H I G A NSTATE

U N I V E R S I Y

T S U N A M I

THE

B TPUZZLE

AND

T H E

R H I C

Scott Pratt The HBT Puzzle and the RHIC Tsunami The HBT Puzzle and the RHIC Tsunami Michigan State University

OUTLINE

• What does HBT Measure?• Models• HBT and the Equation of State

– Dynamical Signatures– Entropy

• Tsunamis, EoS & Viscosity


What does HBT measure?

Determines Shape of f(p,r,t)


HBT Basics

Rout ≈Rside + vΔτ

Rlong

Rside


Blast-Wave Models

Rvz=z/τ

Vx=V(r/R)

Parameters: T, R, V , τ, Δτ

Schnedermann, Sollfrank and HeinzTomasik, Broniowski,Lisa and Retiere,…


Blast Wave Fits

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Lisa and Retiere, PRC 70:044907 (04)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

TherminatorBroniowski et al., nucl-th/0212053


NA49 vs. Therminator

3-dimensional details of blast-wave confirmed


Blast-Wave and the HBT Puzzle

Parameters:T 110 MeVR 13 fmV 0.7c τ 10 fm/c Δτ 3 fm/c

Similar Conclusions:Blast Waves (Lisa-Retiere, Tomasik)TherminatorBuda Lund

Requires Kp spectra

Rapid expansionsudden disintegration


HYDRO

Overall sizes depend on EOS & breakup criteria


Cascade/Boltzmann

More resonances -> softer -> biggerStrings -> softer -> bigger


HBT and the EoS: Dynamical Signature

Leads to: Rout/Rside >> 1


HBT and EoS: Entropy

f (rp)≡

d3r[ f(rp,

rr )]2∫

d3r f(rp,

rr )∫

=π 3/2

(2S+1)dN / d3p

RoutRlongRside

Sizes and spectra give phase space density

Phase space density gives Entropy

dS

dy≅2π ptdpt E∫

dNd3p

52−32

ln(2)−ln[ f (pt)] ±123/2

f (pt)⎡⎣⎢

⎤⎦⎥


HBT and EoS:Entropy

• <f> increases with s1/2

• gives entropy for pions• Rinv and spectra for other species gives total S


Is Lattice Eq. of State excluded?

Range


Total Entropy and the lattice EOS

• Final S consistent with lattice EOS• CRUDE!• Entropy moved from pions to baryons


The HBT puzzle

• Models that fit overall volume (fit entropy)underpredict Rside


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)

- Source ???

Needed: Explanation with consistent dynamical model


Tsunamis at RHIC

vwave = gh

(Bauer and Bertsch, PRL '90)


Modeling Tsunamis at RHIC with Hydrodynamics

Pcs2 =dP

d

H

L

cs2 =0.3

cs2 =constant

Increasing L or decreasing c2mixed -> stronger

tsunami

Resonance Gas


HydrodynamicEvolution

L=2 GeV/fm3,c2

mixed=0.05

τ=1,3,5,7,9,11 fm/c


HBT Radii cmixed2 =0.05

cmixed2 =0.15

Large Rside

for L2 GeV/fm3


Viscosity and Tsunamis:

Txx =Tyy =Tzz =PPerfect Hydro:

Navier-Stokes: Tzz =P−η(2∂zvz−∂xvx−∂yvy)−B∇gv

Israel-Stewart: ∂tTij = −(1 / τ )(Tij −TijN .S .)


Initial-State Asymmetry of Tij

Relativistic Gas:

Classical Longitudinal Fields:

Txx =Tyy =Tzz = / 3

Txx =Tyy =Tzz =−

CGC (Krasnitz, Nara &Venugopalan) : Txx =Tyy ≈ / 2Tzz ≈0

For τ=0.5 fm/c -> Significant strengthening of tsunami


Non-Zero Shear

Even for η s/4π

-> significant strengthening of tsunami


Bulk Viscosity in Mixed RegionK.Paech and S.P., PRC 2006

P

P−B∇gv

-> Significant strengthening of 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

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