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

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

What does HBT measure?

Determines Shape of f(p,r,t)

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

HBT Basics

Rout ≈Rside + vΔτ

Rlong

Rside

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

Blast-Wave Models

Rvz=z/τ

Vx=V(r/R)

Parameters: T, R, V , τ, Δτ

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

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

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

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

NA49 vs. Therminator

3-dimensional details of blast-wave confirmed

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

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

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

HYDRO

Overall sizes depend on EOS & breakup criteria

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

Cascade/Boltzmann

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

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

HBT and the EoS: Dynamical Signature

Leads to: Rout/Rside >> 1

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

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)⎡⎣⎢

⎤⎦⎥

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

HBT and EoS:Entropy

• <f> 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 The HBT Puzzle and the RHIC Tsunami Michigan State University

Is Lattice Eq. of State excluded?

Range

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

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 and the RHIC Tsunami Michigan State University

The HBT puzzle

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

Scott Pratt The HBT Puzzle and the RHIC Tsunami The HBT Puzzle and the RHIC Tsunami 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)

- Source ???

Needed: Explanation with consistent dynamical model

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

Tsunamis at RHIC

vwave = gh

(Bauer and Bertsch, PRL '90)

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

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

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

HydrodynamicEvolution

L=2 GeV/fm3,c2

mixed=0.05

τ=1,3,5,7,9,11 fm/c

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

HBT Radii cmixed2 =0.05

cmixed2 =0.15

Large Rside

for L2 GeV/fm3

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

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 .)

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

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

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

Non-Zero Shear

Even for η s/4π

-> significant strengthening of tsunami

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

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

P

P−B∇gv

-> Significant strengthening of tsunami

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

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