S.P. and J.Vredevoogd, arXiv.org:nucl-th 0809.0089 (2008).
J.Vredevoogd and S.P., arXiv:nucl-th/0810.4325

The Long Slow Deathof the HBT Puzzle
femRoutsoisdceopyRlo
B
Hanbury
goTwissnand an aside

Universal Flow in the First fm/c
Scott PrattMichigan State University

M.Lisa,S.P.,R.Soltz&U.Wiedeman, Ann.Rev.Nucl.Part.Phys.(05)

All the theory you need to know!, qC(P!) ≡N (!
p1 , p!2 )N (!
p1 )N (!
p2 )=!

d3 r SP! (!
r ) |φ(!
q, !
r )|2

GOAL!

SP! (!
r )samples
relative positions
Scott Pratt

Michigan State University

Lifetimes

RoutRlong

Rout ≈ Rside + v⊥ ∆ττ ≈Rlong
vthermRside
vz=z/τ

More explosive --> Smaller Rlong, Rout/Rside
Scott Pratt

Michigan State University

What is the HBT Puzzle?
1. Why do hydro+cascade models fail?
success elliptic flow & spectra hailed as proof of"perfect QCD liquid"some pure hadron cascade models work much better

2. Blast-wave models fit datasuggest very rapid expansion
extremely high breakup density

Scott Pratt

Michigan State University

HBT Puzzle

3-d ideal hydro/URQMD
1-d ideal hydro/cascade

1-d ideal hydro1st order phase transition(L=1.6 GeV/fm3)
τ0=1.0 fm/c

STAR

Scott Pratt

3-d ideal hydro from Bass+Nonaka

Michigan State University

ASIDE
Early Acceleration... related to HBTSinyukov (From God)
Krakow (Free-Streaming)
Li & Bleicher(Pre-hadron potentials)
Scott Pratt

Michigan State University

Flow from Classical Fields
Flux Tubes:
Ez =Bφ =T00 =Tzz =Txx =4gΘ(r − R)/R20

Ez2 /2−T00

T00

Expanding Tubes (Point-Like Source)
Ez = 4gδ(r 2 − τ 2 )

Bφ

T00

Scott Pratt= −Ez

2= (Ez2 + Bφ)/2Tzz= 0Txx= T00 /2Michigan State University

A Gallery of Models
MODELTzz

T⊥dE/dηTr TαβFlux Tube-εε∝τ

01000 Points of Light0

ε/2

constant

0

CGC

0

∝ε/2 ∝constant

0Free-Streaming

0

ε/2

constant

0

Ideal Hydro

ε/3ε/3∝τ-1/30???????

00(Krasnitz,Nara,Venugopolan)

Scott PrattMichigan State University

Universal Flow during first fm/c
Ignoring longitudinal flow,
κ= transverse stiffness=(1/3, 1/2, 1)! Flow depends on κ

Scott Pratt

Michigan State University

Universal Flowduring first fm/c

Including longitudinal flow,⇓!
! Universal Flow!

Scott Pratt

Michigan State University

During thermalization,
10 numbers
4 constraints
survive thermalization
can change instantly

measure of elliptic flow
can develop suddenly

Scott Pratt

Michigan State University!

Universal Radial
Flow
AFTER
thermalization!=1 fm/c
!=0.6
!=0.3
hydro
incoherent fields k = 1/2
coherent fields

Scott Pratt

BEFORE
thermalization

Michigan State University!

Universal EllipticFlow
hydro
incoherent fields k = 1/2
coherent fields

Scott Pratt

Michigan State UniversityLast Universal Flow Slide
Flow for first ~1 fm/c is "universal" if:
Boost-invariant (Bjorken) flow
Traceless stress-energy tensor
κ is function of τ only (not x or y)Initial "flow" for hydro depends only on initial profile,
microscopic structure irrelavant

Scott Pratt

Michigan State Universityτ0=1
τ0=0.1

Scott Pratt

Add Early
Acceleration

Michigan State University

Fix Eq. of StateP

cs2=0.1
First order
Crossovercs2=0εfirst-order

Scott Pratt

Michigan State University

Also see Romatschke 2007

Add Viscosity

IdealViscous

Scott Pratt

Michigan State UniversityShear in QGP phase
 0η
24π =
s4

no initial
anisotropy

Scott Pratt

Michigan State University

Bulk viscosity(near Tc)
 0Bmax24π=
s4

Scott Pratt

Michigan State University

Also see Broniowski et al, PRL 2008

Initial Profile
Wounded nucleon
CGC Drescher etal PRC 2007
Collisional Scaling

Scott Pratt

Michigan State UniversityImprove Coulomb

No Coulomb
Bowler-Sinyukov

Scott Pratt

Michigan State University

What Matters:
Significant
Acceleration < 1 fm/c
ShearEquation of State
Initial Energy Profile
Bulk Viscosity
Correct Coulomb
Pion Fields (Cramer/Miller)
Marginal
Solution to HBT Puzzle:

Conspiracy

Scott Pratt

Michigan State University

ε0 (GeV/fm )3Other Observables
MEAN PT (MeV)

Scott Prattwidth of soft region in EoS
L=0
L=800 MeV*
L=1.6 GeV
stiffness of soft region in EoS
c2s = 0c2s = 0.1*
c2s = 0.2
shear viscosity in parton phase
4πη/s=04πη/s=2*4πη/s=4initially isotropic init. cond.
max. bulk viscosity in soft region
4πB/s=04πB/s=2*4πB/s=4
initial density profile
CGC IC
Wounded Nucleon*Collision Scaling

150
114.5
104.5107
114.5
124.5
289
114.5
106.5
148
124
114.5
109
136
114.5
180

Michigan State University

Must Fit HBT, spectra, flow...
Whack-A-Mole

Scott Pratt

Fixing HBT requires increasing explosivity
Bulk viscosity decreases radial flow
Early flow increases elliptic flow
Viscosity decreases elliptic flow....
Michigan State University

HBT Puzzle: Part II
Blast Wave, Therminator, Buda-Lund...
Fit HBT, spectra...
End up with R≈12 fm, τ≈10 fm/c, v⊥≈0.7c
Suggests:
instantaneous acceleration
breakup density ≈ ρ0

Scott Pratt

Michigan State University

Emission Points
from Cascade

px=300Blast-Wave

Blast wave neglects:
positive x-t correlation -> underpredict Δτanisotropic Tij -> underpredict 〈τ〉
Scott Pratt

For T<m, source size -> constant
proton-pions lose kinetic equilibrium

Michigan State University

Where We StandPHASE I. Discovery
PHASE II. Find “satisfactory” fit to data
PHASE III: Rigorous statement of uncertainty

Scott Pratt

Michigan State University