View
81
Download
2
Category
Preview:
DESCRIPTION
QUARK MATTER SYMMETRY ENERGY AND QUARK STARS. Peng-cheng Chu ( 初鹏程 ) ( INPAC and Department of Physics, Shanghai Jiao Tong University. kyois@sjtu.edu.cn ). Collaborators : Lie- wen Chen (SJTU). Outline. Symmetry energy introduction in quark matter. - PowerPoint PPT Presentation
Citation preview
QUARK MATTER SYMMETRY ENERGY AND QUARK STARS
Peng-cheng Chu(初鹏程 )(INPAC and Department of Physics, Shanghai Jiao Tong
University. kyois@sjtu.edu.cn)
Collaborators:Lie-wen Chen (SJTU)
OutlineSymmetry energy introduction in quark matter.Isospin density-dependent-quark-model.EOS in the Isospin DDQM of Beta-equilibrium strange quark matterProperties of compact star based on the Isospin DDQM.Summary and outlook.
Main References:G.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201
F . Weber ,Progress in Particle and Nuclear Physics 54 (2005) 193-288G.X.Peng,A.Li,U.Lombardo Phys. Rev.C 77,065807 (2008)
Thomas D.Cohen, R.J.Furnstahl, and David K.Griegel Phys.Rev.C 45 X.J.Wen, X.H.Zhong, G.X.Peng, P.N.Shen, P.Z.Ning Phys.Rev.C 72 015204
Motivation to learn
Strange quark matter may be the ground state~
The loop diagram of my work
Maybe 2 solar mass of a compact star
The EoS of quarksThe phenomenological
models of quarks
Constraints of QCD chiral symmetry
Color confinement
The symmetry energy of quarks
Symmetry energy of quark matter.
In quark matter:
The symmetry energy
In hadron matter:
[-3,3] [-1,1][-1,1]
In symmetric quark matter , make
And
Then
Symmetry energy of quark matter.
So we deduce the non-interaction symmetry energy of quark matter
Define the symmetry energy as
We can get the non-interaction symmetry energy of quark matter
Symmetry energy of quark matter.
So we choose the second and discuss the symmetry energy in 3 different models
Density-dependent-quark-model.
Since bag model incorporate the bag constant ,many ways of effective term can be introduced to meet the principle.
Write the Hamiltonian density as:
Use the effective mass to make the form like a non-interacting system:
mq is the effective mass G.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201
The two hamiltonian density must have the same eigenenergy
then
Isospin density-dependent-quark-model.
If we considered as an invariant interacting term for q=u,d or s
Notice that:
Hellmann-Feynman theorem
Give a renormalization-group invariant about quark condensate.
Thomas D.Cohen, R.J.Furnstahl, and David K.Griegel Phys.Rev.C 45
is used in sum-rules as –(225±25MeV)^3 for each flavor of quarks
Isospin density-dependent-quark-model.
Isospin density-dependent-quark-model "+" for d quark, else for u quarkFor s quark , DI = 0.
With this treatment and doing volume
integral :
We check the range of DI
Symmetry energy of quark matter.
G.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201,1999
In Density-dependent-quark-model.
Follow the postulate above ,the symmetry energy is:
The mass is effective mass
Symmetry energy of quark matter.
The symmetric energy vs. baryon number density in CDDM(D^1/2=160Mev, ms=80Mev)
Symmetry energy of quark matter.
The equivalent mass when we take the iso-spin dependence is:
Then the symmetry energy under this isospin DDQM is:
The mass is effective mass
"+" for d quark, else for u quark.
Where
Symmetry energy of quark matter
When DI=0, CDDM and isospin DDQM has the same form
Symmetry energy of quark matter
DI = 1.0 Isospin DDQM
Symmetry energy of quark matter
The symmetry energy vs. baryon number density in Isospin DDQM
Symmetry energy in NJL model
0 4 2i i i i j j k km m G q q K q q q q
We can get the symmetry energy in NJL model
Where i for u,d and s quarks.
22 2 2
3iF
ii k
i
mC k dk
k m
Λ=602.3MeV , G =1.835/602.3^2 , K = 12.36/602.3^5
Symmetry energy in NJL model
2 2 2 2 2 202
, ,
3 2 ( ) 4iF
NJL i u d s u d ski u d s
k m k dk G C C C KC C C
rhoQs = rhoB
rhoQs = 0.
Thermodynamic treatment to EOSNow we calculate the EoS of beta equilibrium quark matter
based on the isospin density dependent quark model.
According to the thermodynamic treatment
2 2
u
j j j jBu u u j j
j ju B j u j
d m v m vnu v m n f n fdn n n m n m
2 23
3 [ 1 ( 1 )]2
f x x x ln x xx
where
Define
Then the chemical potential is
2 24 1 12 2
3 3 3
1 (1 ) 2 2 9 ( ) ( )
jI I d u I d du u u j u d
j j u d u u d dB B B
vD D DD n v DD n vu v m n f n f n f
m n n m n n mn n n
Thermodynamic treatment to EOS
Strange quark matter is considered as a mixture of u,d,s quarks and electrons.
chemical equilibrium:
Baryon density :
Charge-neutrality:
Solve this system of equation ,we can get the elements of the EOS
Thermodynamic treatment to EOS
2 24 1 12 2
3 3
I I
3
1 (1 ) DD DD2 29 ( ) ( )
jI u u u dd d d j d
j j u d u u d d
vD D n v n vu v m n f nu f n fm n n m n n mnB nB nB
And for d,s quark:
2 24
3
1 (1 )9
jIs s s j
j j
vD Du v m n f
mnB
To solve the equations , we make nB given
Mev fm-3 DI=0 DI=0.3 DI=1.0Energy per baryon(min)
919.980 929.018 929.466
Pressure (zero) -.261608 0.923606E-02 -.330257E-01
Energy per baryon’s minimum value and zero pressure plot appear at the same time
Thermodynamic treatment to EoSNow check DI’s effect in the EoS of quark matter
When DI increases , the minimum of the lines increase too.
Thermodynamic treatment to EOSCompare the relationship between the Fermi momentum and chemical potential
DI=0.
DI=0.1DI=0.06.
DI=0.02.
Thermodynamic treatment to EOSCompare the relationship between the quark fraction and rhoB
The properties of Quark star
M/M
⊙
The properties of Quark star
Set Ms0 as the parameter of the quark star while making DI=1.1 & D^1/2=147 MeV
Rotating Quark star
HADRON-QUARK PHASE TRANSITION
HADRONIC PHASE: RMF Theory
where the sum on B runs over the baryon octet :
HADRON-QUARK PHASE TRANSITION
In the RMF model, the meson fields are treated as classical fields, and the field operators are replaced by their expectation values.
Effective mass
HADRON-QUARK PHASE TRANSITION
The coupling constants set TM1 to calculate.
For neutron star matter consisting of a neutral mixture ofbaryons and leptons, the β equilibrium conditions without
trapped neutrinos are given by
HADRON-QUARK PHASE TRANSITION
Then we get the chemical potential of baryons and leptons
The charge neutrality condition is given by
Where
HADRON-QUARK PHASE TRANSITION
At a given baryon density
The total energy density and pressure ofneutron star matter are written by
HADRON-QUARK PHASE TRANSITION
Also the pressure is given as :
Phase transition may occur in the core of massive neutron star.
HADRON-QUARK PHASE TRANSITION
The two crucial equations:
The energy density and the baryon density in the mixed phase are given by
Solve the system of equations , we can get the phase transition diagram, which I haven’t done yet.
HADRON-QUARK PHASE TRANSITION
Particle fraction vs Baryon number density
HYBRID STAR
The mass-radius relation for the hybrid star & Quark star.
OTHER QUARK MODELS
Bag constant for confinement
Quasi-particle bag model
D&T-DQM
Finite temperature may also cause problems.
NJL,PNJL,MIT,CFL,CDM …
Isospin DDQM at Finite temperature:
EoS at Finite Temperature in Isospin DDQM
X.J.Wen, X.H.Zhong, G.X.Peng , P.N.Shen , and P.Z.Ning Phys.Rev.C 72 015204,2005
Summary and outlook.
1. We extend the density-dependent-quark- mass(DDQM) model in which the confinement is modeled by the density-dependent quark masses to include the isospin dependence.
2. We make use of the model we provide to discuss the form of symmetry energy in quark matter. And we discuss the reason why people choose the symmetry parameter.
3. Based on the isospin dependent DDQM model ,we study the symmetry energy of quark matter and the EoS of strange quark matter. And we give the symmetry energy in
NJL model.
4. We give the quark star properties based on the Isospin DDQM and acquire a 2 solar mass quark star.
Get the mass-radius relation for strange stars and study the structure of strange stars with surface effect considered.
We can use RMFT and Isospin DDQM to study the hadron-quark phase transition .
I will study on the stuff about quark matter based on QCD right away.
OUT LOOK
INPAC
Thank you!
Recommended