QCD Phase Transitions QCD Phase Transitions & One of Their Astronomical Signals& One of Their Astronomical Signals

Yuxin Liu （刘玉鑫）Department of Physics, Peking University, China

The CSQCDII, Peking University, Beijing, China, May 20-24, 2009

Outline I. Introduction II. QCD Phase Transitions in DSE Approach III. The Astronomical Signal IV. Summary

In collaboration with: Dr. Lei C. Dr. Zhang Z., Dr. Wang B.,

Dr. Gu J.F., Fu W.J., Chen H., Shao G.Y., ······,

& Dr. Roberts C.D., Dr Bhagwat M.S., Dr. T. Klaehn, .

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

DSE Approach of 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

No pole at real No pole at real axisaxis

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

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

II. Our Work on QCD PT in DSE ApproachII. Our Work on QCD PT in DSE Approach

Effect of the F.-S.-B. (Effect of the F.-S.-B. (m0) on Meson’s Mass ) on Meson’s Mass Solving the 4-dimenssional covariant B-S equation with the kernel being fixed by the solution of DS equation and flavor symmetry breaking, we obtain

( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) )

Composition of the Vacuum of the System with Finite Isospin Chemical PotentialCase 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

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, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009)(2009)))

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

arXiv:0807.3486 (EPJC60, 47(2009) ) gives the 5th solution .arXiv:0807.3486 (EPJC60, 47(2009) ) gives the 5th solution .

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

…………

NJL model

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

Alkofer’s SoluAlkofer’s Solution-2cction-2cc““Alkofer’s Alkofer’s

Solution”Solution”--BCFit1BCFit1

BC vertex

P-NJL Model ofP-NJL Model of （（ 2+12+1 ）） Flavor Quark Flavor Quark System and the related Phase Transitions System and the related 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) )

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)

,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

(L. Chang, Y. X. Liu, H. Guo, Nucl. Phys. A 750, 324 (2005))

Temperature dependence of some properties Temperature dependence of some properties of of and and -mesons in PNJL model-mesons in PNJL model

( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) )

Goldberger-Treiman Relation: 2222 rmgf qq

GM-O-Renner Relation:

rmfmG

m

20

22 01

with

Effects of Quarks and CSC on the Effects of Quarks and CSC on the M-R Relation of Compact Stars M-R Relation of Compact Stars

Many signals have been proposed: e.g., r-mode instability, Larger dissipation rate, Cooled more rapidly, Spin rate more close to Kepler Limit, ······ .

J.F. Gu, H. Guo, X.G. Li, Y.X. Liu, et al.,

Phys. Rev. C 73, 055803 (2006); Eur. Phys. J. A 30, 455 (2006); .

III. The Astronomical Signal of QCD PTIII. The Astronomical Signal of QCD PT

Distinguishing Newly Born Strange Quark Distinguishing Newly Born Strange Quark Stars from Neutron Stars Stars from Neutron Stars

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 pulsation 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. SummaryIV. Summary ： ： QCD Phase TransitionsQCD Phase Transitions With the DSE approach of QCD, we show thatWith the DSE approach of QCD, we show that the vacuum of the system with finite isospin chemical the vacuum of the system with finite isospin chemical

potential contains not only pion condensation but potential contains not only pion condensation but also mixed quark-gluon condensate; also mixed quark-gluon condensate; above a critical coupling strength and bellow a critical above a critical coupling strength and bellow a critical

current mass, DCSB appears; current mass, DCSB appears; meson mass splitting induced by the flavor symmetry meson mass splitting induced by the flavor symmetry breaking is not significant; breaking is not significant; above a criticalabove a criticalμμ, PR-, PR-S occurs & matter appears. S occurs & matter appears. We develop the Polyakov-NJL model for (2+1) We develop the Polyakov-NJL model for (2+1) flavor system and study the phase transitions. flavor system and study the phase transitions. We p We propose a signal of distinguishing the newly ropose a signal of distinguishing the newly born Strange stars from neutron stars, i.e, born Strange stars from neutron stars, i.e, an astronomical signature of QCD PT.an astronomical signature of QCD PT.

Thanks !!!Thanks !!!

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 oscillationOscillations 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.

Chiral Susceptibility & Chiral Susceptibility & PT in NJL ModelPT in NJL Model

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)