Quantum Opacity, RHIC HBT Puzzle, and the Chiral Phase

Transition

• RHIC Physics, HBT and RHIC HBT Puzzle• Formalism• Quantum mech. treatment of optical

potential, U (Chiral symmetry) • Reproducing data, wave function• Summary

Gerald Miller and John Cramer, UW

The RHIC HBT Puzzle Data from the first five years of RHIC Some evidence supports the presence of QGP formed in early stages

of Au+Au collisions: Relativistic hydrodynamics describes the low and medium

energy dynamic collision products

Elliptic flow data implies very high initial pressure and collectivity

Most energetic pions, produced early, strongly suppressed Strong suppression of back-to-back jets.D Au vs Au Au, central vs peripheral

Hydrodynamics worksBUT NOT FOR HBT

qout

qside

qlong

Rsi

de

R long

Rout

p1

p2

p2

+

p2

p1

q

Quantum mechanical interference-space timeseparation of source

q=p1-p2

K=(p1+p2)/2

C(q,K) p1,p2) p1p2))-1 ~ λ(1-q2

L R2L-q2

S R2S –q2

O R2O )

HBT- 2 particle interferometry

Hydrodynamics predicts big RO/RS,

Data RO/RS about 1 HBT puzzle

Time extent of source R2o >>R2

s

t1 + t2

Expect R2o >>R2

s

A highlight from this week

Burt Holzman, PHOBOS

Rs =Ro

Old Formalism source current density =J

Chaotic sources, Shuryak ‘74 S0~<J J*>

σ(p1)

Source Propertieshydrodynamics inspired source function of Wiedemann Heinz et al

S0(x,K) ~freeze out surface

Bjorken tube model-boost invariant

but π emission allowed everywhere

ρ(b) medium density

radial flow

Overview of Our Model Allow pions to be emitted anywhere in

medium, not only at freeze-out surface Pions interact with the matter on their way

out. Pion absorption implemented via

imaginary part of optical potential.

Real part of optical must exist, acts as mass and velocity change of pions due to chiral-symmetry breaking as they pass from the hot, dense collision medium to the outside vacuum

Formalism

• Pions interact U with dense medium

is distorted (not plane) waveGyulassy et al ‘79

DWEF- distorted wave emission function

Wave Equation SolutionsMatter is infinitely long Bjorken tube and azimuthal symmetry, wave functions factorize: 3D

2D(distorted)1D(plane)

We solve the reduced Klein-Gordon wave equation for p:

Partial wave expansion ! ordinary diff eq

Son & Stephanov 2002Son & Stephanov 2002

v2, v2 m2approach near T = Tc

Both terms of U are negative (attractive)

=ω2-m2π

Fit STAR Data

6 source, 3 optical potential parametersFit central STAR data at sNN=200 GeV

reproduce Ro, Rs, Rl

reproduce dNdy (both magnitude and shape) 8 momentum values (i.e., 32 data points)

Fit to 200 GeV Au+Au Radii

U=0

Re U=0

Potential Effects

200 GeV Au+Au Spectrum

U=0

no flow

noBE

Meaning of the Meaning of the ParametersParameters

• Temperature: 193 MeV fixed at phase transition temperature S. Katz, QM05

• Transverse flow rapidity: 1.5 vmax=0.85 c, vav=0.6 c• Pion emission between 6.2 fm/c and 11 fm/c soft EOS .• WS radius: 11.8 fm = R (Au) + 4.4 fm > R @ SPS• Re(U): 0.14 + 0.85 p2 deep well strong attraction.• Im(U): 0.12 p2 mfp 8 fm @ KT=1 fm-1 strong

absorption high density• Pion chemical potential: = mass()

Consistent with CHIRAL PHASE TRANSITION!

Wave Functions |(, b)|b)

KT=100 MeV/c

KT=250 MeV/c

KT=600 MeV/c

DWEF(Full)

DWEF(Im Pot only)

EikonalApprox.

Centrality & Nuclear DependenceAu+Au Cu+Cu

Au+AuCentrality:

0-5%

5-10%

10-20%

20-30%

30-50%

50-80%

Cu+CuCentrality:

0-10%

10-20%

20-30%

30-40%

40-50%

50-60%

Rout Rout

Rside

Rlong

Rside

Rlong

SummaryQuantum mechanics solves technical problems of applying

opacity to HBT.

Excellent fits sNN=200 GeV data: three radii, pT spectrum.

Fit parameters: indicate strong collective flow, significant opacity, and huge attraction. Describe pion emission in hot, highly dense matter (a soft pion equation of state) .

Replace the RHIC HBT Puzzle with evidence for a chiral phase transition. In most scenarios, the QGP phase transition is accompanied by chiral phase transition at about same critical temperature.

• Phys.Rev.Lett.94:102302,2005, nucl-th/0507004

The End

SPARES FOLLOW

The End

For details see:Phys.Rev.Lett.94:102302,2005 and a newer preprint: nucl-th/0507004 , submitted PRC

Source Properties3

0 0( , ) ( , ) ( , ) /(2 )TS x k B b K S2 2

00 2 22

( )cosh( , ) exp2 22 ( )

S

1( , ) ( )exp 1

T TB b K M bK u

T

2 2 2t z

12 ln t z

t z

particle momentum 4-vector trasverse flow 4-vector

Ku

(“hydrodynamics inspired” source function of Heinz & collaborators)

(Bose-Einstein thermal function)

(medium density)

S0(x,K) ~freeze out surface

Correlation/Gaussian Fit

Eikonal Magnitude of wave function

b/R

bl

RO = R/4.48 HV

Correlation Functions

9 Fits: 200 GeV/A Au+Au

2 vs. Temp for 9 Fits