qcd phase transition in dyson-schwinger equation approach
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QCD Phase Transition in Dyson-Schwinger Equation Approach. Yuxin Liu Department of Physics, Peking University Beijing 100871, China. Outline I. Introduction II. Brief View of DSE Approach - PowerPoint PPT PresentationTRANSCRIPT
QCD Phase Transition QCD Phase Transition in Dyson-Schwinger Equation Approachin Dyson-Schwinger Equation Approach
Yuxin Liu
Department of Physics, Peking University
Beijing 100871, China
SQM2008 , Beijing , China , October 6-10, 2008
Outline I. Introduction II. Brief View of DSE Approach III. Some of Our Work IV. Summary
I. IntroductionI. IntroductionThe History of the Universe
Schematic QCD Phase Diagram
Aspects influencing Aspects influencing QCD P.-T. QCD P.-T.Medium : Temperature,
Density ( or )
Finite size
Intrinsic : Current mass,
Coupling Str.,
C-F structure,
••• •••
It relatesConfinement – Deconf.
S Breaking – Restoration
Flavor symmetry breaking
Chiral SymmetricQuark deconfined
SB, Quark confined
sQGP
Theoretical Approaches : Lattice QCD Finite Temperature Field Theory, RG, LT with dynamical theory (model): QHD, (p)NJL, QMC, QMF, QSR, INST, DSE, GCM, ···
Key Points: Representing the two main features of QCD: Chiral Symmetry & its Breaking Confinement
AdS/CFT
II. Brief Description of DSEs in QCDII. Brief Description of DSEs in QCD Dyson-Schwinger Equations
General Point of View
D-S equation is a set of coupled integral
eqs. among quark, gluon, ghost and
vertex functions,
where the n-point function depends on
the (n+1)-and higher point functions.
C. D. Roberts, et al, Prog. Part. Nucl. Phys. 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007,53; R. Alkofer, et. al, Phys. Rept. 353, 281 (2001); .
Rain-Bow Approximation Quark equation at zero chemical potential
where is the effective gluon propagator,
can be conventionally decomposed as)(1 pG
)( qpD freeab
Quark equation in medium
with
Effective Gluon Propagators
(2) Model
(1) MN Model
(2) (3)
(3) More Realistic model
(4) An Analytical Expression of the Realistic Model:
Maris-Tandy Model
(5) Point Interaction: (P) NJL Model
14 )( q
Example of the success of the DSE:
Generation of Dynamical Mass
Phys. Rev. C 68, 015203 (2003)
III. Some of Our Recent WorkIII. Some of Our Recent Work Effect of Current Quark Mass on Meson Effect of Current Quark Mass on Meson MassMass
( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) )
Solving the B-S equation with the kernel being fixed by the solution of DS equationand flavor symmetry breaking, we obtain
parameters are taken From Phys. Rev. D 65, 094026 (1997), with fitted as
Effect of the running coupling strength on Effect of the running coupling strength on the chiral phase transition the chiral phase transition
f MeVf 93
(W. Yuan, H. Chen, Y.X. Liu, (W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 Phys. Lett. B 637, 69 (2006))(2006))
Lattice QCD result Lattice QCD result PRD 72, 014507 (2005)PRD 72, 014507 (2005)
with D = 16 GeV2, 0.4 GeV
Effect of Current Mass on Effect of Current Mass on PT PT
Solutions of the DSE with
Mass function
With =0.4 GeV
16 0.4
L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) (nucl-th/0605058)
Phase Diagram in terms of the Current Mass Phase Diagram in terms of the Current Mass and the Running Coupling Strength and the Running Coupling Strength
Distinguishing the Dynamical Breaking Distinguishing the Dynamical Breaking from the Explicit Breaking from the Explicit Breaking
( L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) )
Effect of the chemical potential dependence Effect of the chemical potential dependence of the gluon propagator on of the gluon propagator on PTPT
Diquark channel:( W. Yuan, H. Chen, Y.X. Liu, ( W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) )Phys. Lett. B 637, 69 (2006) )
Chiral channel:( L. Chang, H. Chen, B. Wang, W. Yuan,( L. Chang, H. Chen, B. Wang, W. Yuan, and Y.X. Liu, Phys. Lett. B 644, 315Y.X. Liu, Phys. Lett. B 644, 315 (2007) )
Components of the vacuum of the system with finite isospin chemical potential Case 1. , , , ;Case 2. , , , ;Case 3. , , , ;Case 4. , , , No Solution.
(Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 035201 (2007))(Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 035201 (2007))
0215 qGiqaca
0 qq 015 qiq maxFF 0 qq 015 qiq 0215 qGiq
aca
maxmin FFF
0 qq 015 qiq 0215 qGiqaca
minFF
0 qq 015 qiq 0215 qGiqaca
Chiral Susceptibility & Chiral Susceptibility & PT in NJL PT in NJL ModelModel
Y. Zhao, L. Chang, W. Yuan, Y.X. Liu, Eur. Phys. J. C 56, 483 (2008)Y. Zhao, L. Chang, W. Yuan, Y.X. Liu, Eur. Phys. J. C 56, 483 (2008)
Phase Diagram of Quark Matter in P-NJL Model
- relation nucleon properties
2
24
2
22
2
21
22
2
6
21
])1(ln[
422 4)(qeq tm
q
QCD
q
m
q
eDqD
0/ BB 0/ RR 0/MM
(W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor)(W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor)
Simple case: 2-flavor, Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) )Simple case: 2-flavor, Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) )
Order of the QCD Phase Transitions Order of the QCD Phase Transitions ( W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor) )( W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor) )
,c PTR ,c PTR
Collective Quantization: Nucl. Phys. A790, 593 (2007).
Nucleon as a Soliton in DSENucleon as a Soliton in DSE
B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007)
Variation of Nucleon Properties with Variation of Nucleon Properties with Respect to the Density of the Matter Respect to the Density of the Matter
- relation nucleon properties
2
24
2
22
2
21
22
2
6
21
])1(ln[
422 4)(qeq tm
q
QCD
q
m
q
eDqD
0/ BB 0/ RR 0/MM
(L. Chang, Y. X. Liu, H. Guo, Nucl. Phys. A 750, 324 (2005))
Phase transition from vacuum to matter
H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, arXiv:0807.2755H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, arXiv:0807.2755
Phase with Phase with SB & Confinement is stable hadron matter SB & Confinement is stable hadron matter appears appears
Distinguishing Newly Born SQS Distinguishing Newly Born SQS From NSFrom NS
W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, to appear in Phys. Rev. Lett.
NS: RMF, SQS: Bag Model
IV. Summary IV. Summary
We discussed the QCD Phase Transitions ;We discussed the QCD Phase Transitions ;
running coupling strong enough, running coupling strong enough,
current mass lower than a critical value, current mass lower than a critical value, Dynamical chiral symmetry breaking Dynamical chiral symmetry breaking
Matter can be generated from vacuum Matter can be generated from vacuum
through the chiral phase transition through the chiral phase transition
Fundamental & Quite Perspective ! Fundamental & Quite Perspective ! Great efforts are still required ! Great efforts are still required !
Thanks !!!Thanks !!!
M+ shifts upward too.
Three different solutions exist in chiral limit
M+ shifts upward too.
Chang, Liu, et al., Phys. Rev C 75, 015201 (2007)
Chang, Liu, et al., Phys. Rev C 75, 015201 (2007)
Chang, Liu, et al., Phys. Rev C 75, 015201 (2007)
Shape of NucleusShape of Nucleus
Sphere
Deforemation quadrupole octupole hexadecupole
3/10ArR
]),(1[ *0
kmkmkmYRR
Modes of Nuclear Collective Motion vibration & GR
axial rotation ( prolate, oblate)
-soft rotation
triaxial rotation ••• ••• ••• •••
E. S. Paul et al. , Phys. Rev. Lett. 98 , 012501 (2007)