Phase Transitions of Strong InterPhase Transitions of Strong Interaction System action System

in Dyson-Schwinger Equation Approachin Dyson-Schwinger Equation Approach

Yu-xin Liu （刘玉鑫）Department of Physics, Peking University, China

第 13 届全国中高能核物理大会，中国科技大学，合肥， 2009 年 11 月 5-7 日

Outline I. Introduction II. The Approach III. Some Numerical Results of Our Group IV. Summary & Outlook

I. IntroductionI. Introduction

Schematic QCD Phase Diagram

Items Affecting the PTsItems Affecting the PTs::

Medium Effects ： Temperature, Density (Chem. Potent.) Finite size Intrinsic Effects ： Current mass, Run. Coupl. Strength, Color-Flavor Structure, ••• •••

Related Phase Transitions:Confinement(Hadron.) –– DecconfinementChiral Symm. Breaking –– CS RestorationCS RestorationFlavor Symmetry –– Flavor Symm. Breaking

Chiral SymmetricQuark deconfined

SB, Quark confined

sQGP

How do the aspects influence the phase transitions ?

Why there exists partial restoration of dynamical S in low density matter ?

How does matter emerge from vacuum ?

Theoretical MethodsTheoretical Methods ： Lattice QCD Finite-T QFT, Renormal. Group, Landau T., Dynamical Approaches （ models ） : QHD, (p)NJL, QMC , QMF, QCD Sum Roles, Instanton models, Dyson-Schwinger Equations (DSEs),

General Requirements for the approaches: not only involving the chiral symmetry & its breaking ,

but also manifesting the confinement and deconfinement .

AdS/CFT

Slavnov-Taylor Identity

Dyson-Schwinger Equations

axial gauges BBZ

covariant gauges QCD

II. The DSE Approach of II. The DSE Approach of QCDQCD

C. D. Roberts, et al, PPNP 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007), 53; R. Alkofer, et. al, Phys. Rep. 353, 281 (2001); C.S. Fischer, JPG 32(2006), R253; .

Practical Way at Present Stage 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 Meeting the requirements!

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 Cuchieri, et al, PRL, 2008

Models of Vertex

(1) Bare Vertex

(2) Ball-Chiu Vertex

(3) Curtis-Pennington Vertex

),( pq(Rainbow-Ladder Approx.)

For Hadron StructureFor Hadron Structure

(2) Soliton Model (non-local fields)(2) Soliton Model (non-local fields)

(1) Bethe-Salpeter Equation approach(1) Bethe-Salpeter Equation approach

Examples of achievements of the DSE of QCDExamples of achievements of the DSE of QCD Generation of Dynamical Mass

Taken from: The Frontiers of Nuclear Science – A Long Range Plan (DOE, US, Dec. 2007). Origin: MSB, CDR, PCT, et al., Phys. Rev. C 68, 015203 (03)

Taken from: Tandy’s talk at Morelia-2009

More recent result for the mass splitting

between

ρ& a1 mesons

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)

Point Point InteractionInteraction

S PhaseS Phase

III. Some Numerical Results of Our GroupIII. Some Numerical Results of Our Group Chiral Susceptibility (Chiral Susceptibility (S & S & SB phases simultaneously): SB phases simultaneously): Signature of the Chiral Phsae Transition Signature of the Chiral Phsae Transition

parameters are taken From Phys. Rev. D 65, 094026 (1997), with fitted as

Effect of the Running Coupling Strength Effect of the Running Coupling Strength on the Chiral Phsae Transition on the Chiral Phsae Transition

f MeVf 93

(W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006))(W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006))

Lattice QCD result Lattice QCD result PRD 72, 014507 (2005)PRD 72, 014507 (2005)

((BC Vertex: L. Chang, YXL, RDR, Zong, et al., Phys. Rev. C 79, 035209 (‘09)BC Vertex: L. Chang, YXL, RDR, Zong, et al., Phys. Rev. C 79, 035209 (‘09)))

Bare vertexBare vertexCS phaseCS phase

CSB CSB phasephase

with D = 16 GeV2, 0.4 GeV

Effect of the Current Quark Mass on the Effect of the Current Quark Mass on the Chiral Phase Transition Chiral Phase Transition

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)

Distinguishing Distinguishing the Dynamical Chiral Symmetry Breaking the Dynamical Chiral Symmetry Breaking From Fromthe Explicit Chiral Symmetry Breakingthe Explicit Chiral Symmetry Breaking

( L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) )

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

BC vertex gives qualitatively same results.

Euro. Phys. J. C 60, 47 (2009) gives the 4th solution .Euro. Phys. J. C 60, 47 (2009) gives the 4th solution .

Hep-ph/0612061Hep-ph/0612061 confirms the confirms the existence of the existence of the 3rd solution, 3rd solution, and give the 4th and give the 4th solution .solution .

Effect of the Chemical Potential on theEffect of the Chemical Potential on the Chiral Phase Transition Chiral Phase Transition

Diquark channel:( W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) )( W. Yuan, H. Chen, Y.X. Liu, 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) )

Chiral Susceptibility Chiral Susceptibility

of Wigner-Vacuum of Wigner-Vacuum in DSEin DSE

Some Refs. of DSE study on CSC

1. D. Nickel, et al., PRD 73, 114028 (2006);

2. D. Nickel, et al., PRD 74, 114015 (2006);

3. F. Marhauser, et al., PRD 75, 054022 (2007);

4. V. Klainhaus, et al., PRD 76, 074024 (2007);

5. D. Nickel, et al., PRD 77, 114010 (2008);

6. D. Nickel, et al., arXiv:0811.2400;

…………

Partial Restoration of Dynamical S & Matter Generation

H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, Phys. Rev. D 78, 116015 (2008);H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, Phys. Rev. D 78, 116015 (2008);H. Chen, W. Yuan, YXL, JPG 36 (special issue for SQM2008), 064073 (2009)H. Chen, W. Yuan, YXL, JPG 36 (special issue for SQM2008), 064073 (2009)

Bare vertexBare vertex

BC vertexBC vertex BC vertexBC vertex

BC vertexBC vertexCSB phaseCSB phase

BC vertexBC vertexCS phaseCS phase

NJL ModelAlkofer’s Solution-2cc

Alkofer’s Solution-BCFit1Solution with BC vertex

,c PTR ,c PTR

Collective Quantization: Nucl. Phys. A790, 593 (2007).

Properties of Nucleon in DSE Soliton ModelProperties of Nucleon in DSE Soliton Model

B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007)

Model of the effective gluon propagatorModel of the effective gluon propagator

Density Dependence of some Properties of Density Dependence of some Properties of Nucleon in DSE Soliton Model Nucleon in DSE Soliton 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

(Y. X. Liu, et al., Nucl. Phys. A 695, 353 (2001); NPA 725, 127 (2003); NPA 750, 324 (2005) )

Chemical Potential Dependence of Chemical Potential Dependence of NN

L. Chang,Y. X. Liu, H. Guo, Phys. Rev. D 72, 094023 (2005)

In BC vertex: N N = (= (60~80) MeV 。

Newly result(H. Chen, YXL,et al., to be published) :

Temperature Dependence of the Temperature Dependence of the Propagators of Gluon and Ghost Propagators of Gluon and GhostLattice QCD Results (A. Maas, et al., EPJC 37, 335 (2004);

A. Cucchieri, et al., PRD 75, 076003 (2007) ):

Previous DSE solutions in torus momentum space do not give the same results (C.S. Fischer, et al., Ann. Phys. 321, 1918 (2006); ··· ) .

with

Our Newly Results in continuum Our Newly Results in continuum momentum space momentum space

Solving coupled

equations of

gluon and ghost:

3.1,4.0,1 tgl(H. Chen, R. Alkofer, Y.X. Liu, to be published)

Phase Diagram of Strong Interaction Phase Diagram of Strong Interaction Matter Matter

S.X. Qin, L. Chang, Y.X. Liu, to be published.S.X. Qin, L. Chang, Y.X. Liu, to be published.

Result in bare vertex Result in Ball-Chiu vertex

(GeV)

Phase Diagram of the （ 2+1 ） Flavor System 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

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) )(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)

An Astronomical Signal Identifying the An Astronomical Signal Identifying the QCD Phase Transition QCD Phase Transition

W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, Phys. Rev. Lett. 101 ， 181102 (2008)

Neutron Star: RMF, Quark Star: Bag Model Frequency of Frequency of g-mode oscillationg-mode oscillation

Taking into account the Taking into account the SB effectSB effect

Ott et al. have found that these g-modepulsation of supernova cores are very efficient as sources of g-waves (PRL 96, 201102 (2006) )

DS Cheng, R. Ouyed, T. Fischer, ·····

The g-mode oscillation frequency can be a signal to distinguish the newly born strange quark stars from neutron stars, i.e, an astronomical signal of QCD phase transition.

IV. Summary & DiscussionIV. Summary & Discussion ： ：

We propose an astronomical signal manifesting the quark We propose an astronomical signal manifesting the quark

deconfinement phase transition in dense matter. deconfinement phase transition in dense matter.

We develop the Polyakov-NJL model for (2+1) flavorWe develop the Polyakov-NJL model for (2+1) flavor system and study the phase transitions. system and study the phase transitions.

above a criticalabove a criticalμμ, , S can be restored partially. S can be restored partially.

above a critical coupling strength and below a critical above a critical coupling strength and below a critical current mass, DCSB appears; current mass, DCSB appears;

QCD Phase Transitions:QCD Phase Transitions: With the DSE approach of QCD, we show thatWith the DSE approach of QCD, we show that

A mechanism is proposed !A mechanism is proposed !

Driving the Polyakov-loop from DSE ?!?!

Being checked in sophisticated DSE approach !Being checked in sophisticated DSE approach !

The finite-T effect on the pure gauge fields are given. The finite-T effect on the pure gauge fields are given.

Thanks !!!Thanks !!!

Phase diagram of strong interaction matter (T-Phase diagram of strong interaction matter (T-μμ)) ?! ?!

背景简介背景简介( F.Weber, J.Phys.G 25, R195 (1999) )

Composition of Compact Stars

Calculations of the g-mode oscillationCalculations of the g-mode oscillation Oscillations of a nonrotating, unmagnetized and fluid star ca

n be described by a vector field , and the Eulerian (or “local”) perturbations of the pressure, density, and the gravitational potential, , , and .

( , )r t

p

Employing the Newtonian gravity, the nonradial oscillation equations read

We adopt the Cowling approximation, i.e. neglecting the perturbations of the gravitational potential.

Factorizing the displacement vector as , one has the oscillation equations as

where is the eigenfrequency of a oscillation mode;

is the local gravitational acceleration.

( , ) i tr lmY e

g

The eigen-mode can be determined by the oscillation Eqns when complemented by proper boundary conditions at the center and the surface of the star

The Lagrangian density for the RMF is given as

Five parameters are fixed by fitting the properties of the symmetric nuclear matter at saturation density.

For a newly born SQS, we implement the MIT bag model for its equation of state. We choose

, and a bag constant .

The equilibrium sound speed can be fixed for an equilibrium configuration, with baryon density , entropy per baryon , and the lepton fraction being functions of the radius.

B

S LY

ec

( taken from Dessart et al. ApJ,645,534,2006 ).

We calculate the properties of the g-mode oscillations of newly born NSs at the time t=100, 200 and 300ms after the core bounce, the mass inside the radius of 20km is 0.8, 0.95, and 1.05 MSun , respectively.

We assume that the variation behaviors of and for newly born SQSs are the same as for NSs.

S LY

As ω changes to 100.7, 105.9, 96.1 Hz, respectively.

When MSQS = 1.4Msun , ω changes to 100.2, 91.4, 73.0 Hz, respectively.

As MSQS = 1.68Msun , ω changes to 108.8, 100.9, 84.5 Hz, respectively.

S 1.5S

The reason for the large difference in the g-mode oscillation eigenfrequencies between newly born NSs and SQSs, is due to

The components of a SQS are all extremely relativistic and its EOS can be approximately parameterized as

are highly suppressed.