July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 1

Future Directions in HBT

• This title has been used before• These predictions are seldom right

Title

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 2

HBT-Puzzle For Dummies

• Some very smart people have contributed to our understanding of HBT

• They just don’t care to be associated with it anymore

Possible copyright infringement suit!

Title #2

and by one, but not of…

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July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 3

Solving the HBT Puzzle:Noble quest or trivial pursuit

• I will try to convince you of the former• But, some will remain unconvinced …

For those of you in this category- watch for embedded trivia questions- answer all correctly and collect your beer(s)

Final Title

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 4

Volumes & Lifetimes2nd Law Thermodynamics

• Ideal Gas

• Relativistic Fermi/Bose Gas=0

• Pions (3) vs. QGP (37)

NkTPV =

3

2

)(1523

87 )(

cfb VTnnShπ+=

0

3),,( 0

=

=−+

f

b

nn πππ

24

162322

82

=

=×××

×

flavorcolorspin

colorspin

f

b

n

n

.3

370

constT

qgphadronize VVt

S

=⎥⎦

⎤⎢⎣

⎡ ×≥⇒>∂∂

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 5

HBT (GGLP) Basics• In the simplest approximation, the technique has not

changed since before most of you were bornGoldhaber, Goldhaber, Lee, and Pais, PR 120:300 (1960)

• For identical bosons/fermions

But this (plane wave) approximation neglects many effects

P(p1,p2;r1,r2) =

P(p1,p2)/P(p1)P(p2) = 1 + | (p1 - p2) |2~

Gaussian source in xi yields Gaussian correlation in conjugate variable qi=p1i-p2i

Who made first use of this pedagogic picture?

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 6

HBT Complexities

• We have neglected– Final state interactions

• Coulomb interaction

• Strong interaction

• Weak decays

– Position-momentum correlations– Things more subtle, such as special relativity

State of the art analysis incorporates most of these, but not all

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

1/Rside

Who performed first “correction” for Coulomb?

Where is the first mention of Lorentz effects in HBT?

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 7

HBT - current state of the art

• Bowler/Sinyukov factorization– Assumes |C+C

*|2 = FC •|+*|2

– Still an approximation to 2-3% for kaons

~50 ways to handle Coulomb/Weak decays

All subsequent data shown use the first technique

• Direct Fit– Symmetrized Coulomb waves– See M.Heffner QM04

P. Chung et al, PRL 91:162301 (2003)• Source Imaging, D. Brown–No factorization–No Gaussian assumption

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 8

HBT Radius Definitions (b=0)

• Rlong ~ F

• Rside kT ~ Rgeo

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

• Rout || kT

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 9

HBT Radius Dynamics

• Transverse Expansion profile

• Transverse Freeze-out profile

•Positive x-p correlations reduce all R • Hydrodynamic : ~ x ; R~1/√mT

• Heisenberg : ~ 1/x ; R~1/mT

•Positive x-t correlations=>reduce Rout

R2out = x2 t)2 xt

“inside-outside” cascade

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 10

HBT Experimental Results

• Excellent agreement (phobos too)

• Systematics well under control

• A Precision Tool !

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 11

More Experimental SystematicsSTAR PRL 93:12301 (2004)PHENIX nucl-ex/0401003

Don’t tell me HBT radii don’t relate to a physical size

b≠0

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 12

Model Comparison (the puzzle)

• No model correct• Does Rout/Rside of

unity imply no long-lived mixed phase?

the puzzle

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 13

Model Calculation Systematics

• Each theory paper has explored systematic changes in at least one important variable

– Tf = Freeze-out Temp/profile

– Tc = Critical Temp.

– el = parton scattering cross-section

– E = Latent Heat/transition order

– Tch = chem. Freeze-out temp

– n = viscoscity (-20% Rout, -60% Rlong)D. Teany, nucl-th/0301099

Instead of looking for correct answer, explore systematics

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 14

HBT radii vs. S(x,p) and x-t corr.

• Using x-rms incorrect (at least for low kT pions)

1. Extract radii or check for equivalence2. Freeze-out matters

•x-t term comparable to x and t

Z. Lin et al, PRL 89:152301 (2002)

What was the first reference to explore x-t correlations in a cascade model?

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 15

Partonic cross-sections

Variation in radii for reasonable el/opacity less than sys. errors

• AMPT shows little sensitivity for el=3,6,10,16 mb

D. Molnar and M. Gyulassy, PRL 92:052301 (2004)

significantlyreducedopacity

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 16

Tc in hybrid model

• Results for kaons

• Lower TC 160 vs. 200 MeV

– shortens hadronic phase– E ~ 1.5 vs. 2.9 GeV

– slight drop Rout

– ~20% drop in Rout/Rside

S. Soff, et al., PRL 88:072301 (2002)

Rout/Rside sensitive to TC & latent heat

RO

RS

RL

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 17

Tf & latent heat in chiral model

• --- TF = 130 MeV, --- TF = 80 MeV

• Predictions for Rside and Rout only

• Significant drop in Rout/Rside for 2nd order transition

D. Zschiesche, PRC 65:064902 (2002)

Rout/Rside sensitive to TF and transition order

E=0 GeV

E=1.7 GeV

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 18

3D w/ Tch with hybrid approach

• Rlong nailed !

• Sudden freeze-out may be too sudden but 2D Hybrid has larger Rlong,side

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 19

Review of Models

• Rout/Rside is particularly sensitive to freeze-out dynamics, perhaps uniquely so– could be used to “tune” freeze-out profile– better to calculate with re-scattering model

• Radii sensitive to E and TC and TF

• No evidence yet for strong dependence on partonic phase, except perhaps at higher pT

In a physical model, all these things are coupled

trivial pursuit

noble quest

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 20

Solving the Puzzle

• First

– abandon sudden freeze-out

• Second

– run 3D hydro with small E, low TC, and short hadronic re-scattering phase to define freeze-out

• Ultimate Goal

– run hydro hybrid to map out complete 2 complete parameter space for realistic EOS and init. cond. comparing to full set of observables

How much person and computing power would this require?

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 21

A job for parameterizations?

• Can parameterizations be used to speed up mapping of the 2 space?– Maybe– Worth investigating

First benchmark parameterizations to full calculations

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 22

And for the experiments…

• Extend asHBT to higher kT >0.5 GeV

– more complete test of spatial evolution

• Extend pion radii to higher kT > 1 GeV

– more sensitive to pre-hadronic phase• Extend to kaons, protons

– investigate meson/baryon dynamics• HBT with 2-photons

– probe early dynamics

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 23

The proton-proton “conundrum”

• Evidence for same expansion dynamics in p-p collisions

• Are we seeing a universal property of particle production?

• Maybe - this is not (yet) a precision test

• 4 bins is not enough to study differences in dynamics

Rout / Rout(pp) Rside / Rside(pp)

Rlong / Rlong(pp)

T. Gutierrez, nucl-ex/0403012 (2004)

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 24

Solving the Puzzle

• First

– abandon sudden freeze-out

• Second

– run 3D hydro with small E, low TC, and short hadronic re-scattering phase to define freeze-out

• Ultimate Goal

– run hydro hybrid to map out complete 2 complete parameter space for realistic EOS and init. cond. comparing to full set of observables

How much person and computing power would this require?

July 22, 2004 R. Soltz, Hot Quarks, Taos, NM 25

Size & LifetimeBose-Einstein Correlations