Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition
description
Transcript of Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition
![Page 1: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/1.jpg)
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
![Page 2: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/2.jpg)
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
![Page 3: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/3.jpg)
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
![Page 4: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/4.jpg)
Time extent of source R2o >>R2
s
t1 + t2
Expect R2o >>R2
s
![Page 5: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/5.jpg)
A highlight from this week
Burt Holzman, PHOBOS
Rs =Ro
![Page 6: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/6.jpg)
Old Formalism source current density =J
Chaotic sources, Shuryak ‘74 S0~<J J*>
σ(p1)
![Page 7: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/7.jpg)
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
![Page 8: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/8.jpg)
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
![Page 9: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/9.jpg)
Formalism
• Pions interact U with dense medium
is distorted (not plane) waveGyulassy et al ‘79
DWEF- distorted wave emission function
![Page 10: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/10.jpg)
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
![Page 11: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/11.jpg)
Son & Stephanov 2002Son & Stephanov 2002
v2, v2 m2approach near T = Tc
Both terms of U are negative (attractive)
=ω2-m2π
![Page 12: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/12.jpg)
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)
![Page 13: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/13.jpg)
Fit to 200 GeV Au+Au Radii
U=0
Re U=0
![Page 14: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/14.jpg)
Potential Effects
![Page 15: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/15.jpg)
200 GeV Au+Au Spectrum
U=0
no flow
noBE
![Page 16: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/16.jpg)
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!
![Page 17: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/17.jpg)
Wave Functions |(, b)|b)
KT=100 MeV/c
KT=250 MeV/c
KT=600 MeV/c
DWEF(Full)
DWEF(Im Pot only)
EikonalApprox.
![Page 18: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/18.jpg)
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
![Page 19: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/19.jpg)
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
![Page 20: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/20.jpg)
SPARES FOLLOW
![Page 21: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/21.jpg)
The End
For details see:Phys.Rev.Lett.94:102302,2005 and a newer preprint: nucl-th/0507004 , submitted PRC
![Page 22: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/22.jpg)
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
![Page 23: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/23.jpg)
Correlation/Gaussian Fit
![Page 24: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/24.jpg)
Eikonal Magnitude of wave function
b/R
bl
RO = R/4.48 HV
![Page 25: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/25.jpg)
Correlation Functions
![Page 26: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/26.jpg)
9 Fits: 200 GeV/A Au+Au
![Page 27: Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition](https://reader036.fdocuments.us/reader036/viewer/2022070421/56816348550346895dd3d946/html5/thumbnails/27.jpg)
2 vs. Temp for 9 Fits