Hadron to Quark Phase Transition Hadron to Quark Phase Transition

in the Global Color Symmetry Model in the Global Color Symmetry Model

of QCDof QCD

Yu-xin Liu

Department of Physics, Peking University

Collaborators: Guo H., Gao D.F., Chang L. Wang B.,

Song H.C., Chao J.Y. et al., at PKU;

Wang F., Zong H.S., et al., at NJU;

Lue X.F. at SCU;

Zhao E.G. at ITP; Chao W.Q. at IHEP.

Outline

I. Introduction

II. The Framework

III. Numerical Results

IV. Remarks

I. IntroductionI. Introduction Two Puzzles in Current Physics (in T.D. Lee’s words):

Chiral Symmetry and its Spontaneous Breaking

Color Confinement

Characteristics Identifying

Quark Deconfinement

and Chiral Symmetry

Restoration:

Hadron Properties

Vacuum Structure

Lattice QCD, pQCD (Factorization, Re-summation), •••

Confinement Mechanism:Flux Tube, Center Vertex, ···Intuitive view?

NJL model, QMC, QMF, Truncated DSE, Instanton, GCM, ···

How the Chiral Symmetry is Restored ? Quark condensates are usually taken as characteristics of Vacuum Structure Order Parameters. Theoretical approaches: Composite-operator, Sum rules, QMC, Walecka model, Dirac-Brueckner, S-D Equation, Instanton dilute liquid model, …

Different results have been obtained!!

Chi. Sym.

C S B

(Comp.-Op., PRD41,1610(’90) ) ( QSR, NP A642, 171 (’98) )

(D-S Eq. PR C55, 1577(’97) ) (DS Eq. PR C57, 2821(’98) ) (IDLM, NP A642, 83(’98) )

(Walecka, PR C55, 521 (‘97))

Hadron Properties are essential in describing finite

nuclei and strong interaction matter

Effective mass

EMC effect, nuclear structure & reaction

Nucleon swell EMC effect

Bag constant Quark confinement

Theoretical Approaches:

Bag Models, QMC, QMF

bag constant, bag energy, radius

Phenomenologically!

QCD foundation ??? the GCM appears

*M

II. The Framework of the GCMII. The Framework of the GCM 1. The Main Point of Global Color Symmetry Model

R.T. Cahill, C.D. Roberts, Phys. Rev. D 32 (1985) 2419

Lue, Liu, Zhao, Zong, Phys. Rev. C 58 (1998) 1195

Prog. Part. Nucl. Phys. 39 (1997) 117; Phys. Rev. D49 (1994) 125; Phys. Rev. C53 (1996) 2410; ······ .

Effective degrees of freedom becomes quark and chiral mesons

2. GCM in Strongly Interacting Matter

Tniiq n )12(4

q q q q q q

3. The Scalar Quark Condensates

4. The mass and decay constant of pion

5. Relation Between the Chemical Potential and the Density

GCM, Global Color Symmetry Model: an effective field theory model of QCD

Truncated DSE NJL, ChPT QCD GCM Hadronisation Observables BM, QMC, QHD Lattice Hadron Correlation

With the GCM, one can explore the QCD foundation of bag models, the chiral symmetry breaking and restoration, the quark confinement and deconfinment, ••••••••••.

III. Numerical ResultsIII. Numerical Results

New approach to determine the vacuum configuration of the GCM

B = m in instanton model

Property of pion and sigma meson

Lue, Liu, Zhao, Zong, Phys. Rev. C 58 (1998) 1195

Relation between Relation between and and

)( 431

2

2

Nucleon bag constantNucleon bag constant

B(0)=(172 MeV)4

Y. X. Liu, et al, Nucl. Phys. A 695 (2001) 353, A 725 (2003) 127

Nucleon radius and massNucleon radius and mass

R(0)=0.7 fm m(0)=939 MeV

Y. X. Liu, et al, Nucl. Phys. A 695 (2001) 353; A725 (2003) 127.

Quark condensatesQuark condensates In nuclear matterIn nuclear matter

3)148(:: MeVqq

Y. X. Liu, et al, Phys. Rev. C68 (2003), 035204.

With a full gluon propagator

- 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/ BB0/ RR 0/MM

Y. X. Liu, et al, Nucl. Phys. A 750 (2005), 324.

quark condensate

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

-0.03

-0.02

-0.01

0.00

0.01

0.02

second first zero

T (GeV)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400.000

0.005

0.010

0.015

0.020

0.025T=30MeVT=60MeVT=70MeVT=90MeV

<qq

>

Quark Gluon mixed CondensateQuark Gluon mixed Condensate

Zhao Zhang, Wei-qin Chao, Phys. Lett. B 610 (2005), 235

The effective potential at and

00T

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

20s13s

20s12s

20s11s

30s

GeV

fm420

quark confinement results from the self-adjustment among/between quarks

The effective potential at finite and The effective potential at finite and

quark deconfinement and chiral symmetry

restoration may take place

T

The mass and decay constant of pionThe mass and decay constant of pion

Susceptibilities:Zong H. S. et al., Phys. Lett. B 557 (2003) 33Zong H. S. et al., Phys. Lett. B 576 (2003) 289Zong H. S. et al., Phys. Rev. D 67 (2003) 074004Zhang Z., Chao W.Q., Phys. Lett. B 612 (2005) 207

Axial vector vertexZong H. S. et al., Phys. Rev. C 66 (2002) 015201

New Approach to Evaluate the Quark Propagator at Finite Chemical Potential

Zong, Chang, Hou, Sun, Liu, Phys. Rev. C 71 (2005) 015205

IV. Remarks IV. Remarks The density dependence of the bag constant, the mass and radius of nucleons and the pion mass and decay constant are studied in an effective field theory model of QCD， namely the GCM The scalar local and nonlocal quark condensates are also investigated.

Calculated result 1: with the increase of the density

before a critical value is reached, the BN and MN

decrease, the M almost maintains constant, the RN,

the f and the condensates increase.

Calculated result 1: with the increase of the density before a critical value is reached, the BN and MN decrease, the M almost maintains constant, the RN, , , the f and the condensates increase.

Calculated result 2: at the critical density, the BN and MN vanish gradually, the M , f and the , etc, disappear suddenly, the RN becomes infinite.

Quark deconfinement and the chiral symmetry restoration phase transitions happen at the critical density.

Chiral symmetry restoration process: broken more strongly gradually, at least, at the same scale, then restored suddenly.

qq Gqq

qq

Thanks !!!Thanks !!!