light-front dynamic application to the rhic physics korea university, june 16, 2007 in collaboration...
DESCRIPTION
Outline Brief Overview on State Changes Chemical and Thermal Freeze-outs Hadronization Mechanisms Quark Recombination and Fragmentation Numerical Results Wavefunction Dependence on P T Spectra, Ratio between proton and antiproton, etc... Elliptic Flow Preliminary V 2 calculation ConclusionTRANSCRIPT
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Light-Front Dynamic Application to the RHIC Physics
Korea University, June 16, 2007In collaboration with Prof. Byungsik Hong
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Motivation• QGP is thought to have existed ten millionths of second after the Big Bang; creating the primordial matter of universe in the laboratory.
• RHIC obtained distinguished results from CERN SPS._ Jet Quenching and Bulk Hadronization (BARYONS07)• LHC ALICE (CMS, ATLAS) would need theoretical predictions at energy 30-fold energy increase from RHIC.
• LFD has progressed last several years._ Trecherous points exist and correct use is required.
Time to investigate the application and make a progress….
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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...• Elliptic Flow Preliminary V2 calculation • Conclusion
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Nuclear Phase DiagramT(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 ~2014
SPS(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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QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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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 T≫ C ≈ 175 MeV
• Heavy Ion Collision- Hard Scattering and High PT Fragmentation
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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
ρπ
FormalismFunction in Wigner ),()(
where
),)1(;(|),(|),;()2()2(
)(
)2
;()()2
;()2()2(
)(
3
23
2
3
3
3
3
3
3
3
∫
∫ ∫
∫ ∫
Φ=Φ
−−⋅
=
+Φ−⋅
=
⊥+
⊥⊥+
Σ
⊥+
Σ
qrrdq
kPxRwkxkxPRwkdPdxRuPRdC
qPRwqqPRwqdRuPRdCPd
dNE
WM
WM
bMaM
bWMaM
M
ψππ
ππ
)(),(),();(
0
2//)( 22
rrφrφrγ η
−Θ≈= Δ−⋅−
ffeeπRw TRvπ
aa
R.Fries,B.Muller,C.Nonaka and S.Bass, PRC68, 044902(2003); PRL90, 202303(2003)
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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
baTMyT
M
η
ψηγγπ
nbaPower
baGauss
xkm
xkmkx
xkm
xkmkx
)1
/(1),(
]/)1
([Exp),(
22222
22222
aψ
bψ
+−+
++
=
−+
++
−=
⊥⊥⊥
⊥⊥⊥
B.Hong, C.Ji, D.-P.Min, PRC73, 054901 (2006)
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Light-Front Wavefunctions
ψK
x
k⊥
ψD
x
k⊥
ψπ
x
k⊥
β2 (GeV2) = 0.026 0.26 2.6
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Gaussian vs. Power Law)2,5.0( 2 == nPower aψ π
)825.0( 2 =bψ πGauss
)1,825.0( 2 == nPower aψ π
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Ref.8: R.Fries,B.Muller,C.Nonaka,S.Bass,PRC68,044902(2003)
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Fragmentation and Jet Quenching
k)/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 function
B.A. Kniel, et al., NPB 582, 514 (2000)D. De Florian, et al., PRD 57, 5811 (1998)
ATTT R
Lpbpbp ><=Δ )(),( e
R. Baier, et al., JHEP 0109, 033 (2001)B. Mueller, PRC 67, 061901 (2003)
Striking results from STAR:BARYONS07
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Single Spectra of Mesons
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Single Spectra of Baryons
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Comparison of Particle Ratios
--- R.Fries,B.Muller,C.Nonaka,S.Bass,PRC68,044902(2003) B.Hong,C.Ji,D.-P.Min,PRC74,054901(2006)
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Enhanced sea quark contribution to the fragmentation of p and pbar.
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Enhanced sea quark contribution to the fragmentation of p.
We do not expect for the recombination model to work for peripheral collisions.
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Enhanced sea quark contribution to the fragmentation of pbar.
We do not expect for the recombination model to work for peripheral collisions.
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Particle Ratios Data for central Au+Au collisions at √sNN
= 200 GeV
Open Squares: PHENIX Data-Phys. Rev. C 69, 034909 (2004)
Solid Circles: STAR Data-Phys. Rev. Lett. 97, 152301 (2006)
Solid Lines: Predictions by the present recombination model by using the fragmentation function determined by the
pp collisions data
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Anisotropy Parameter v2 Elliptic flow = v2 = 2nd Fourier coefficient of momentum anisotropy
dn/df ~ 1 + 2 v2(pT) cos (2f) + …Initial spatial anisotropy is converted into momentum anisotropy. Efficiency of the conversion depends on the properties of the medium
f
x
yz
f
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Elliptic Flow Calculation
€
v2M (PT )=
dx∫ d 2k⊥ |ψ(x,k⊥ )|2 {v2
a(xPT + k⊥ )+v2b[(1−x)PT −k⊥ ]}kM (x,k⊥ ,PT )
dx∫ d 2k⊥ |ψ(x,k⊥ )|2 {1+ 2v2
a(xPT + k⊥ )v2b[(1−x)PT −k⊥ ]}kM (x,k⊥ ,PT )
NR⏐ → ⏐ v2a(12PT )+v2
b(12PT )
1+ 2v2a(12PT )v2
b(12PT )
€
v2a( πT )= cos(2φ) =
dφcos(2φ)I2[ πT sinηηT (φ)∫ / T] K1[mT cosηηT (φ)/T]
dφ I0[ πT sinηηT (φ)∫ / T] K1[mT cosηηT (φ)/T]
€
ηT (φ)=ηT0 [1−f(πT )cos(2φ)] ; f( πT )=
a n
1+ (πT / π0)m ; a =
w(b)−l(b)w(b)+ l(b)
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Anisotropy Parameter v2
Au+Au at √sNN = 200 GeV
Data- Open Symbols for negatives- Solid Symbols for positives
Recombination model-No fragmentation-Dashed lines: α=0.50-Solid lines: α=0.42-Dotted lines: α=0.35
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Anisotropy Parameter v2
Au+Au at √sNN = 200 GeV
Data- Open Symbols for negatives- Solid Symbols for positives
Recombination model-Explicit model calculation for protons by the recombination for pT>4 GeV/c is still underway.-For preliminary result here, we assumed the simple quark number scaling for now. -Including the fragmentation part-Dashed lines: Recombination-Dotted lines: Fragmentation-Solid lines: Sum
preliminary
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Conclusions and Outlook• Extended the formulation of recombination model
– Intrinsic Transverse Momentum Effect– Light-Front Wavefunction
• Gaussian vs. Power Law• Found the sensitivity of wavefunction dependence
– Recombination favored by the larger size hadrons• New results on yield ratios of K-/K+ and pbar/p
– Jet Quenching Effect included• Elliptic flow Extension possible and preliminary results obtained• Maybe useful for the analysis of other QGP nature
– Possible Formation of the Binary Systems– Crossover between BCS and BEC
• Feshbach Resonances – Heavy Hadron Production
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Food for Thoughts:Binary Bound States in QGP
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Effective Mass
Pressure
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.