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)