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2005-06-27 The 6th Heavy Ion Meeting 1
Quark Recombination and Quark Recombination and FragmentationFragmentation
C. R. JiIn collaboration with
Profs. B. Hong and D.-P. Min
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Motivation of HI Collisions
QGP is thought to have existed ten millionths of second after the Big Bang; creating the primordial matter of universe in the laboratory.
2. High-energy nuclear collisions will compress and heat the heavy nuclei so much that their individual protons and neutrons overlap and lots of pions arise, creating the Quark-Gluon Plasma (QGP)
1. Quarks and Gluons exist, but not detected individually at T=0. Temperature Dependence of Confinement and Chiral Symmetry
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3. RHIC obtained distinguished results from CERN SPS.– Jet Quenching and Bulk Hadronization (Winner of recent NSAC meeting).
4. LHC ALICE (CMS, ATLAS) would need theoretical predictions at energy 30-fold energy increase from RHIC.
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Outline• Brief Overview on State Changes
Chemical and Thermal Freeze-outs• Hadronization Mechanisms
Quark Recombination and Fragmentation• Numerical Results
Wavefunction Dependence on PT Spectra, Ratio between proton and antiproton, etc...
• Discussion and Conclusion BCS-BEC Crossover, Heavy quark systems, etc...
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Simulation by the Frankfurt Group
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• Expansion and Cooling
- T → TC• Hadronization from QGP- Intermediate PT (2-5 GeV) Recombination
• Chemical Equilibrium and Freeze-out (TC ≈ 175 MeV)- Inelastic Channels (e.g. Δ↔pπ)- Number of each hadron species doesn’t change
• Thermal Equilibrium - Elastic Scatterings Dominant- Interaction still exists (MFP > DBP)• Continued Expansion and Thermal Freeze-out
- Particle distance gets larger (DBP > MFP)- No further elastic collisions but still heavy particles can decay into light particles (e.g. Δ→Ρπ): Tfreeze-out≈120 MeV
• Formation of QGP - T ≫ TC ≈ 175 MeV
• Heavy Ion Collision- Hard Scattering and High PT Fragmentation
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Nuclear Phase Diagram
T(MeV)
Density(n0)
~150
~10
Early Universe(RHIC)
Color SuperconductorNeutron Star
Hadron Gas
Quark-Gluon Plasma
Phase Transition
Atomic NucleiSIS explores high baryon density hadronic matter.
RHIC & future LHC explore high temperature & low baryon density partonic matter.
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Heavy-Ion AcceleratorsAccelerator c.m. Energy
(GeV)Status
SIS 18(GSI, Germany)
2A(A=mass number)
Running
AGS(BNL, USA) 5A Finished
SIS 300(GSI, Germany) 8A Plan to run from
~2014SPS
(CERN, Switzerland) 20A Finish soon
RHIC(BNL, USA) 200A Running
LHC(CERN, Switzerland) 5500A Plan to run from
~2007
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Relativistic Heavy Ion Collider
Brookhaven National Lab.Brookhaven National Lab. in New Yorkin New York
Circumference: 3.83 km First collision: 2000 100A GeV Au+Au(2X1026/cm2/s) 250 GeV p + p (2X1032/cm2/s)
PHENIPHENIXX STARSTAR
PHOBOPHOBOSS
BRAHMBRAHMSS
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Hadronization MechanismsR.J. Fries, nucl-th/0403036, PRC 68, 044902 (2003)
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Recombination of a Quark-Antiquark Pair
PMPMPdN abab
M ;|ˆ|;)2( 3
3
FormalismFunction in Wigner ),()(
where
),)1(;(|),(|),;()2()2(
)(
)2
;()()2
;()2()2(
)(
3
23
2
3
3
3
3
3
3
3
qrrdq
kPxRwkxkxPRwkdPdxRuPRdC
qPRwqqPRwqdRuPRdCPd
dNE
WM
WM
bMaM
bWMaM
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)(),(),();(
0
2//)( 22
ffeepRw TRvp
aa
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Extended Recombination Formalism
22221
21
0 0
203
02
)1()(cosh),,(
where
),,(),(sinh2)2(
kPxmkxPmT
KPkxk
PkxkkxkddxT
PIVMCdyPd
dN
TbTaT
TM
TMTT
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nbaPower
baGauss
xkm
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22222
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Light-Front Wavefunctions
ψK
x
k⊥
ψD
x
k⊥
ψπ
x
k⊥
β 2 (GeV2) = 0.026 0.26 2.6
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Gaussian vs. Power Law)2,5.0( 2 nPower )825.0( 2
Gauss
)1,825.0( 2 nPower
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Fragmentation and Jet Quenching
)/1(
)(
02
1
0 323
BpCK
dypddN
pddNEzD
zdz
PddNE
TyT
perta
a a
aaha
h
- Parameters of the parton distribution function
D.K. Srivastava, et al., PRC 67, 034903 (2003)
- Parameters of the Fragmentation functionB.A. Kniel, et al., NPB 582, 514 (2000)D. De Florian, et al., PRD 57, 5811 (1998)
ATTT R
Lpbpbp )(),(
R. Baier, et al., JHEP 0109, 033 (2001)B. Mueller, PRC 67, 061901 (2003)
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Numerical Results1. Single Particle Spectra2. Particle Ratios3. Nuclear Modification Factor Rcp4. Wave Function Dependence
Gaussian vs. Power Law
5. Prediction for D-meson Production at RHIC and LHC
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Single Spectra
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Comparison of Particle Ratios
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Comparison of Particle Ratios
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Comparison of Particle Ratios
Fries et al., PRC 68, 044902 (2003)
Fries et al., PRC 68, 044902 (2003)
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Comparison of Nuclear Modification
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Comparison of Nuclear Modification
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Gaussian vs. Power Law
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Heavy Quark Distribution FunctionRHIC
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Heavy Quark Distribution FunctionLHC
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Prediction of D-Meson Spectra
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Conclusions and Outlook• Extended the formulation of the recombination model
– Intrinsic transverse momentum effect– Light-Front wavefunction
• Gaussian vs. Power Law• Found the sensitivity of the wavefunction dependence
– Recombination is favored by the larger size hadrons• Different results on the yield ratios of K-/K+ and pbar/p
– Jet quenching effect is included• Our extended formulation may be useful for the analysis of
the QGP nature– Possible formation of the binary system – Crossover between BCS and BEC via Feshbach resonances
• Plan to investigate – Heavy hadron production– Elliptic flow
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Food for Thoughts:Binary Bound States in QGP
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Effective M
assPressure
T/Tc
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Bose-Einstein Condensation
Hydrodynamical Expansion of Trapped Atoms
Analogous to Elliptic Flows in RHIC Data
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Crossover between BCS and BEC
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Controlling Parameters
• High Tc Superconductors: Doping Holes• Ultracold Trapped Atoms: Applying Magnetic Fields • RHIC: Changing sNN and Projectiles, etc.