Transcript QCD Phase Transitions & One of Their Astronomical Signals Yuxin Liu （刘玉鑫） Department of Physics, Peking University, China In collaboration with: Dr.

QCD Phase Transitions
& One of Their Astronomical Signals
Yuxin Liu （刘玉鑫）
Department of Physics, Peking University, China
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, .
Outline
I. Introduction
II. QCD Phase Transitions in DSE Approach
III. The Astronomical Signal
IV. Summary
The CSQCDII, Peking University, Beijing, China, May 20-24, 2009
I. Introduction

How do theQCD
aspectsPhase
influence
the phase transitions ?
Schematic
Diagram
 Why there exists partial restoration of dynamical S in
Related Phase Transitions:
low density matter ?
Confinement(Hadron.)
 How does matter emerge
from vacuum ? –– Decconfinement
Chiral Symmetric
Quark deconfined
sQGP
Chiral Symm. Breaking
–– CS Restoration
Flavor Symmetry
–– Flavor Symm. Breaking
Items Affecting the PTs:
SB, Quark confined
Medium Effects：
Temperature,
Density (Chem. Potent.)
Finite size
Intrinsic Effects：
Current mass,
Run. Coupl. Strength,
Color-Flavor Structure,
Theoretical 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), 
AdS/CFT
General Requirements for the approaches:
not only involving the chiral symmetry & its breaking ,
but also manifesting the confinement and deconfinement .
DSE Approach of QCD
Dyson-Schwinger Equations
Slavnov-Taylor Identity
axial gauges
covariant gauges
BBZ
QCD
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 Dabfree ( p  q) is the effective gluon propagator,
G 1 ( p) can be conventionally decomposed as
 Quark equation in medium
No pole at real axis
Meeting the requirements!

with
 Effective Gluon Propagators
(1) MN Model
1
(2) (q  ) Model
4
(2)
(3)
(3) More Realistic model
(4) An Analytical Expression of the Realistic Model:
Maris-Tandy Model
(5) Point Interaction: (P) NJL Model
Examples of achievements of the DSE of QCD
Generation of Dynamical Mass
Taken from:
Tandy’s talk
at Morelia-2009
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)
II. Our Work on QCD PT in DSE Approach
 Effect of the F.-S.-B. (m0) 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 Potential
a
Case 1.  q q  0 ， q i 51q  0 ,  q i 5 1  G
a
Case 2.  q q  0 ,  q i 51q  0 ,  q i 5 1  G
ac
 q q  0 ， q i 51q  0 ， q i 5 1  Ga
Case 4.  q q  0 ， q i 51q  0 ,  q i    G
ac
Case 3.
a
5 1
2
ac
2
2
ac
2
q  0 ， F  Fmax ；
q  0 ，Fmin  F  Fmax ；
q  0 ,
q  0
F  Fmin ；
，No Solution.
(Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 035201 (2007))
 Effect of the Running Coupling Strength
on the Chiral Phsae Transition
(W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006))
parameters are taken From Phys. Rev. D 65, Lattice QCD result
094026 (1997), with f fitted as f  93MeV PRD 72, 014507 (2005)
Bare vertex
CS phase
CSB
phase
(BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009))
 Effect of the Current Quark Mass on the
Chiral Phase Transition
L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007)
(nucl-th/0605058)
Solutions of the DSE with
Mass function
  0.4
  16
With =0.4 GeV
with D = 16 GeV2,   0.4 GeV
Distinguishing
the Dynamical Chiral Symmetry Breaking From
the 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
and the Running Coupling Strength
Hep-ph/0612061
confirms the existence of the
3rd solution, and give the 4th
solution .
arXiv:0807.3486 (EPJC60, 47(2009) ) gives the 5th solution .
Effect of the Chemical Potential on the
Chiral Phase Transition
Chiral channel:
( L. Chang, H. Chen, B. Wang, W. Yuan, and Y.X. Liu, Phys. Lett. B 644, 315 (2007) )
Diquark channel:
( W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) )
Chiral Susceptibility
of Wigner-Vacuum
in 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
BC vertex
CSB phase
Bare vertex
BC vertex
BC vertex
BC vertex
CS phase
NJL
BCmodel
Alkofer’s
“Alkofer’s
vertex
Solution-2cc
Solution”-
BCFit1
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)
 P-NJL Model of（2+1）Flavor Quark
System and the related Phase Transitions
( 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
(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) )
B / B0
D(q )  4 D  6 e
2
- relation
2
q2
R / R0
2
 q2


4 2 m
2
1 ln[  (1 q
2
QCD
M / M0

q2
1 e 4 mt
2
q2
)
]
2
2
nucleon properties
 Properties of Nucleon in DSE Soliton Model
Model of the effective gluon propagator
Rc,  PT
Rc,  PT
B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007)
Collective Quantization: Nucl. Phys. A790, 593 (2007).
 Density Dependence of some Properties of
Nucleon in DSE Soliton Model
(L. Chang, Y. X. Liu, H. Guo, Nucl. Phys. A 750, 324 (2005))
R / R0
B / B0
D(q )  4 D  6 e
2
- relation
2
q2
2
 q2


4 2 m
2
1 ln[  (1 q
2
QCD
M / M0

q2
1 e 4 mt
2
q2
)
]
2
2
nucleon properties
 Temperature dependence of some properties
of  and -mesons in PNJL model
Goldberger-Treiman Relation:
f2 g2qq  m2r 2
GM-O-Renner Relation:

m2 f2  m0   1 2Gm0 
r
with
( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) )
III. The Astronomical Signal of QCD PT
 Effects of Quarks and CSC on the
M-R Relation of Compact Stars
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);  .
Many signals have been proposed:
e.g., r-mode instability, Larger dissipation rate, Cooled more rapidly,
Spin rate more close to Kepler Limit, ······ .
 Distinguishing Newly Born Strange Quark
Stars from Neutron Stars
Neutron Star: RMF, Quark Star: Bag Model
Frequency of g-mode oscillation
W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084,
Phys. Rev. Lett. 101， 181102 (2008)
Taking into account the SB effect
Ott et al. have found
that these g-mode
pulsation 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. Summary：
 QCD Phase Transitions
With the DSE approach of QCD, we show that
 the vacuum of the system with finite isospin chemical
potential contains not only pion condensation but
also mixed quark-gluon condensate;
 above a critical coupling strength and bellow a critical
current mass, DCSB appears;
 meson mass splitting induced by the flavor symmetry
breaking is not significant;
 above a criticalμ, PR-S occurs & matter appears.
 We develop the Polyakov-NJL model for (2+1)
flavor system and study the phase transitions.
 We propose a signal of distinguishing the newly
born Strange stars from neutron stars, i.e,
an astronomical signature of QCD PT.
Thanks !!!
Composition of Compact Stars
背景简介
( F.Weber, J.Phys.G 25, R195 (1999) )
Calculations of the g-mode oscillation

Oscillations of a nonrotating, unmagnetized and fluid star
can be described by a vector field  (r, t ) , and the Eulerian
(or “local”) perturbations of the pressure, density, and the
gravitational potential,  p ,  , and  .

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
rYlm ( , )eit
 is the eigenfrequency of a oscillation mode;
g is the local gravitational acceleration.
,

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.

The equilibrium sound speed ce can be fixed for an
equilibrium configuration, with baryon density  B , entropy
per baryon S , and the lepton fraction YL being functions of
the radius.
( taken from Dessart et al. ApJ,645,534,2006 ).

For a newly born SQS, we implement the MIT bag model
for its equation of state. We choose
, and a bag constant
.

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 S and YL for
newly born SQSs are the same as for NSs.
 As
S
1.5S
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.

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 & PT in NJL Model
Y. Zhao, L. Chang, W. Yuan, Y.X. Liu, Eur. Phys. J. C 56, 483 (2008)