Quantum Opacity, RHIC HBT Puzzle, and the Chiral Phase Transition

Quantum Opacity, RHIC HBT Puzzle, and the Chiral Phase Transition

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

potential, U (Chiral symmetry) , DWEF

• Reproducing π data

• Summary, future plans Phys.Rev.Lett.94:102302,2005

and J.Phys.G34:703-740,2007

Gerald Miller and John Cramer, UW

The RHIC HBT Puzzle The RHIC HBT Puzzle Pratt’s talk- can’t fit entropy

and HBT radii with same model

Hydrodynamics works

BUT 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-q2L R2

L-q2S R2

S –q2O R2

O )

HBT- 2 particle interferometry

Hydrodynamics predicts big RO/RS,

Data RO/RS about 1 HBT puzzle

Old Formalism

source current density =J

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

σ(p1)

Source Properties “Hydro-Inspired” Emission Function

Source Properties “Hydro-Inspired” Emission Function

30 0( , ) ( , ) ( , ) /(2 )TS x k B b K S

2 20

0 2 22

( )cosh( , ) exp

2 22 ( )

S

1( , ) ( )

exp 1T TB b K M b

K u

T

2 2 2t z

1

2ln

t z

t z

particle momentum 4-vector

flow 4-vector

K

u

(Bose-Einstein thermal function)

(medium density)

(Space-time function)

includes radial flow

Formalism

• Pions interact U with dense medium

is distorted (not plane) waveGyulassy et al ‘79

DWEF- distorted wave emission function

U - self energy

U :phenomenological-not from equil. thermo, J

Wave Equation SolutionsWave 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:

U time independent, cylindrical, Partial wave expansion ! ordinary diff eq

Meaning of U

Im (U) : Opacity, Re (U) :Refraction

pions lose energy and flux Re(U) must exist. Next:very strong attractionchiral phase transition

Chiral Symmetry, Son & Chiral Symmetry, Son & Stephanov 2002Stephanov 2002

v2, v2 m2approach near T = Tc

Both terms of U are negative (attractive)

=ω2-m2π

OverviewOverview Pions emitted anywhere, any time, not only at freeze-

out surface Pions interact with the surroundings during escape . These interactions not included in the source

function S- No relation between U and S Quarks, gluons are the dominant source of the

pions, but not the cause of U Im [U] accounts for opacity Re[U] must exist, causes refraction, acts as mass-change

of pions due to chiral-symmetry breaking as they pass from the hot, dense collision medium [m()0]) to the outside vacuum [m()140 MeV].

Relativistic quantum mechanics , solve pion wave equation with partial wave expansion.

Time-Independence,Resonances, and Freeze-

Out

Time-Independence,Resonances, and Freeze-

Out Use of a time-independent phenomenological optical potential does not invoke the mean field approximation and represents an average over a duration The effects of the optical potential disappear as the system decays.

The optical potential also includes the effects of resonances, including the heavy ones.

Heavy resonances decay into π’s outside of the plasma. We account for this by computing only that part of the spectra that is related to the pions in the HBT correlation functionλ parameter accounts for these

Recent CorrectionsRecent Corrections1. We discovered in November a convergence vs. integration

step size problem in our calculation of optical model wave functions. This had no effect on the HBT radii, but had a strong effect on the slope of the spectrum. This problem was corrected by changing from Runge-Kutta to Numerov wave function solutions.

2. We discovered in March that the effects of the strong chemical potential was being applied to the spectrum, but not to the HBT radii. This error was corrected. M. Luzum (UW)

3. The net result, after refitting, is that the “ambiguities” mentioned previously are gone, and the emission temperature of the model has dropped from T=193 MeV to T=161 MeV. The need for a very deep and absorptive optical potential remains.

4. Result: The New Improved DWEF Model (DWEF v.2.1).

Fit STAR DataFit STAR Data6 source, 3 optical potential parametersFit central STAR data at sNN=200 GeVT=160 MeV, μπ =pion mass

reproduce Ro, Rs, Rl

reproduce dNdy (both magnitude and shape) 8 momentum values (i.e., 32 data points)Correct spectrum for contribution of resonances

decaying outside the target

100 200 300 400 500 6003

4

5

6

7

8

100 200 300 400 500 6000.95

1

1.05

1.1

1.15

1.2

1.25

100 200 300 400 500 600

33.5

44.5

55.5

66.5

100 200 300 400 500 600

33.5

44.5

55.5

66.5

DWEF Fits toSTAR 200 GeV Pion HBT Radii

DWEF Fits toSTAR 200 GeV Pion HBT Radii

KT (MeV/c)

RO(fm)

RS(fm)

KT (MeV/c)

RL(fm)

RO/RS

KT (MeV/c) KT (MeV/c)

Temperature is about 160 MeV

100 200 300 400 500 600 700

50

100

500

1000

100 200 300 400 500 600

4

5

6

7

8

100 200 300 400 500 600

4

5

6

7

8

Components of DWEF Calculations

Components of DWEF Calculations

Red Solid - Full DWEFYellow Dots - Plane wave (U=0, no flow)Green Short Dash - Re( p^2 term) only, no flowAqua Long Dash - Im(p^2 term) only, no flowCyan Dot Dash - Re(Const term) only, no flowBlue 2-Dot Dash - Flow only, U=0Violet 3-Dot Dash - DWEF with no BE correction

KT (MeV/c)

KT (MeV/c)

RO(fm)

RS(fm)

KT (MeV/c)

SpectrumdN

2/2MTdMTdy

100 200 300 400 500 600 700

20

50

100

200

500

DWEF Fit toSTAR 200 GeV Pion

Spectrum

DWEF Fit toSTAR 200 GeV Pion

Spectrum

Note: accurate predictionof spectrum slope involvessubtle cancellations among wavefunctions

KT (MeV/c)

SpectrumdN

2/2MTdMTdy

Meaning of the Meaning of the ParametersParameters

Meaning of the Meaning of the ParametersParameters

• Temperature: 160 MeV • Transverse flow rapidity: 1.2 vmax=0.83 c, vav=0.6 c• Pion emission between 6.2 fm/c and 11 fm/c soft

EOS .• WS radius: 12 fm = R (Au) + 4.4 fm > R @ SPS• Re(U): 0.5 + 0.85 p2 deep well strong attraction

size consistent with chiral phase transition (.49 +1 p2).• Im(U): 0.13 p2 mfp 8 fm @ KT=1 fm-1 strong

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

Optical Wave Functions [||2(b)]

Optical Wave Functions [||2(b)]

KT =250 MeV/c

KT =600 MeV/c

KT =100 MeV/c

EikonalApprox.

Observer

DWEF

100 200 300 400 500 600

3

4

5

6

7

100 200 300 400 500 600

2

3

4

5

100 200 300 400 500 600

3

3.5

4

4.5

5

5.5

6

6.5

Centrality: 200 GeV Au+Au

Centrality: 200 GeV Au+Au

RO(fm)Au+Au Fit

Au+Au Predictions

RL(fm)Au+Au Fit

Au+Au Predictions

RS(fm)Au+Au Fit

Au+Au Predictions

Space-time parameters RWS, aWS, are scaled by participant number. Emission duration is constant.

Red: Central Collisions . . .Indigo: Peripheral Collisions

KT (MeV/c)

KT (MeV/c)

KT (MeV/c)

100 200 300 400 500 600

2

3

4

5

6

7

100 200 300 400 500 600

2

3

4

5

100 200 300 400 500 600

2

3

4

5

6

Centrality: 200 GeV Cu+Cu

Centrality: 200 GeV Cu+Cu

Cu+Cu Predictions

Cu+Cu Predictions

Cu+Cu Predictions

Space-time parameters RWS, aWS, are scaled by participant number. Emission duration is scaled as A1/3.

Red: Central Collisions . . .Indigo: Peripheral Collisions

RO(fm)Au+Au Fit

RS(fm)Au+Au Fit

RL(fm)Au+Au Fit

KT (MeV/c)

KT (MeV/c)

KT (MeV/c)

10 20 30 40 50 60 70

56789

101112

10 20 30 40 50 60 70200

500

1000

2000

5000

10 20 30 40 50 60 70

510152025303540

10 20 30 40 50 60 70

510152025303540

Low pT Behavior:Ramsauer Resonances in

Well

Low pT Behavior:Ramsauer Resonances in

Well

KT (MeV/c)

Phobos 0-6%

KT (MeV/c)

RO (fm) RS (fm)

RL (fm)Spectrum

dN2/2MTdMTdy

Summary and PlansSummary and Plans

• Quantum mechanical treatment of opacity and refraction

• Excellent fits- many parameters• Parameters of U consistent with chiral phase

transition, but no relation between U and S implemented

• Other tests needed- lower energy data –John

v2 Matt Luzum, UW