quantum opacity, rhic hbt puzzle, and the chiral phase transition rhic physics, hbt and rhic hbt...
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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
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