[PPT] - ScalarIsovector -meson in RMF Theory and the Quark Deconfinement PowerPoint Presentation

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Scalar–Isovector δ-meson in RMF Theory and the Quark Deconfinement Phase Transition in Neutron Stars G.B.Alaverdyan

Yerevan State University, Armenia

Int. Symp. “The Modern Physics of Compact Stars”
Sept. 17-23, 2008, Yerevan

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Introduction

RMF-theory:

J.D.Walecka, Ann.Phys. 87, 4951, 1974 B.D.Serot, J.D.Walecka, Int.J.Mod.Phys. E6, 515, 1997.

σω ρ σω ρ δ

S.Kubis, M.Kutschera, Phys. Lett., B399,191,1997. B.Liu, V.Greco, V.Baran, M.Colonna, M.Di Toro, Phys. Rev. C65, 045201, 2002.

Low density asymmetric nuclear matter: Heavy ion collisions at intermediate energies:

V.Greco, M.Colonna, M.Di Toro, F.Matera, Phys. Rev. C67, 015203, 2003 V.Greco et al., Phys. Lett. B562, 215, 2003. T.Gaitanos, M.Colonna, M.Di Toro, H.H.Wolter, Phys.Lett. B595, 209,2004.

σω ρ δ

.

Neutron stars without quark deconfinement:

σω ρ δ

B.Liu, H.Guo, M.Di Toro, V.Greco, arXiv Nucl-th/0409014 v2, 2005

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Lagrangian density of many-particle system of p,n.σ,ω,ρ,δ

( )

2 2 2 2 2 2

1 ( ) ( ) ( ) ( ) 2 1 1 1 ( ) ( ) ( ) ( ( )) ( ) ( ) ( ) ( ) 2 2 4 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) , 2 2 4

µ µ ω µ ρ µ σ δ µ µ µν µ σ ω µ µν µ µ µν µ δ ρ µ µν

ψ γ ω τ ρ σ τ δ ψ σ σ σ σ ω ω δ δ δ ρ ρ ⎡ ⎤ ⎛ ⎞ = ∂ − − ⋅ − − − ⋅ + ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ + ∂ ∂ − − + − Ω Ω + + ∂ ∂ − + −

N

N N N N

i g x g x m g x g x x x m x U x m x x x x x x m x m x x R x R x L

p N n

ψ ψ ψ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

( ), ( ), ( ), ( )

x

x x x

µ µ

σ ω δ ρ

( , , , )

µ

= = x x t x y z

3 4

( ) ( ) ( ) , 3 4

N

b c U m g g

σ σ

σ σ σ = + Scalar Vector Isoscalar

σ ω

Isovector

δ ρ ( ) ( ) ( ), ( ) ( ) ( ). Ω = ∂ −∂ ℜ = ∂ −∂ x x x x x x

µν µ ν ν µ µν µ ν ν µ

ω ω ρ ρ

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Relativistic mean-field approach

2 * 2 (3) 2 * 2 (3)

1 ( ) , 2 1 ( ) , 2

ω ρ ω ρ

= + + ω + ρ = + + ω − ρ

p p n n

e k k m g g e k k m g g

2

( ) ,

σ σ

σ ⎛ ⎞ σ = + − ⎜ ⎟ σ ⎝ ⎠

s p sn

dU m g n n d

( )

2

,

ω ω

ω = +

p n

m g n n

( )

2 (3)

,

δ δ

δ = −

s p sn

m g n n

( )

2 (3)

1 , 2

ρ ρ

ρ = −

p n

m g n n

* (3) * (3)

, .

σ δ σ δ

= − σ − δ = − σ + δ

p N n N

m m g g m m g g

3 3 2 2

, , 3 3 = = π π

Fp Fn p n

k k n n

* 2 2 2 * 2

1 , = π +

∫

F p

k p s p p

m n k dk k m

* 2 2 2 * 2

1 . = π +

∫

F n

k n sn n

m n k dk k m

( ) ( ( )) x x

µ µ

φ φ ∂ ∂ − ∂ = ∂ ∂ ∂ L L

2 * 2 (3) 2 * 2 (3)

1 ( ) , 2 1 ( ) . 2

ω ρ ω ρ

µ = = + + ω + ρ µ = = + + ω − ρ

p p F p F p p n n F n F n n

e k k m g g e k k m g g

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Parametric EOS for nuclear matter

(3) (3)

, , , , g g g g ≡ ≡ ≡ ≡

σ ω δ ρ

σ σ ω ω δ δ ρ ρ

2 2 2 2

, , ,

ρ σ ω δ σ ω δ ρ σ ω δ ρ

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ≡ ≡ ≡ ≡ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ g g g g a a a a m m m m

,

n p

n n n α − =

the asymmetry parameter

13 13

( )(1 ) 2 2 2 2 2 2 3 2 ( )(1 ) 2 2 2 2 2 2 3 2 2 2 2 2

1 ( , ) ( ) (1 ) ( ) ( ) 1 ( ) (1 ) ( ) ( ) 1 ( ) . 2

−α +α σ ω δ ρ

⎛ ⎞ α = − α + − σ − δ − + − σ − δ + ⎜ ⎟ π ⎝ ⎠ ⎛ ⎞ + + α + − σ + δ − + − σ + δ − ⎜ ⎟ π ⎝ ⎠ ⎛ ⎞ σ ω δ ρ − σ + − + − + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

∫ ∫

F

F

k n F N N k n F N N

P n k n m k m k dk k n m k m k dk U a a a a

13 13

( )(1 ) 2 2 2 2 ( )(1 ) 2 2 2 2 2 2 2 2

1 ( , ) ( ) 1 1 ( ) ( ) , 2

−α +α σ ω δ ρ

ε α = + − σ − δ + π ⎛ ⎞ σ ω δ ρ + + − σ + δ + σ + + + + ⎜ ⎟ ⎜ ⎟ π ⎝ ⎠

∫ ∫

F

F

k n N k n N

n k m k dk k m k dk U a a a a

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Parameters of RMF theory

, , , , , a a a a b c

σ ω δ ρ

( 0 ) α =

Symmetric nuclear matter Saturation density

( ) n n =

*

,

N N

m m = γ (1 )

N

m = − σ γ ( ,0) ( , ) , ,

N n n

n d n B m f f dn n A

= α=

ε ε α = = + =

Binding energy per baryon

( )

2 2

1 ( ) ( )

ω =

+ − + − σ

N F N

a m f k n m n

2 2

( ) ( )

N F N

a n m f k n m

ω

ω = = + − + −σ

( ) 2 2 3 2 2 2

( ) 2 ( )

F

k n N N N

m k dk bm c a k m − = − − + −

∫

σ

σ σ σ σ π σ

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Parameters of RMF theory

2 2

1 ( , ) ( ) 2

sym

d n E n n d

α=

ε α = α

2

( )

sym sym

E n n ε = α

Symmetry energy

2 2 2

( , ) 9 ( )

n n

d n K n dn n

= α=

ε α =

compressibility module

( ) 2 2 2 2 3 4 2 2

2 1 ( ) ( ) 3 4 2

ω σ

⎛ ⎞ σ ε = + = + − σ + σ + σ + + ⎜ ⎟ π ⎝ ⎠

∫

F

k n N N N

b c n m f k m k dk m n a a

938,93

N

m MeV =

*

0,78

N N

m m γ = =

3

0,153 n fm− = 16,3 f MeV = − 300 K MeV =

(0)

32,5

sym

E MeV =

15,372 13,621 11,865 10,104 8,340 6,569 4,794 3 2.5 2 1,5 1 0,5 15,372 13,621 11,865 10,104 8,340 6,569 4,794 3 2.5 2 1,5 1 0,5

2

a fm

ρ 2

a fm

δ 2

a fm

ρ 2

a fm

δ

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Parameters of RMF theory Parameters

σωρ σωρδ

aσ , fm2 9.154 9.154 aω , fm2 4.828 4.828 aδ , fm2 2.5 aρ, fm2 4.794 13.621 b , fm-1 1.654 10-2 1.654 10-2 c 1.319 10-2 1.319 10-2

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Properties of asymmetric nuclear matter

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Properties of asymmetric nuclear matter

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Characteristics of β-equilibrium npe- plasma

( , , ) ( , ) ( ),

NM e e e

n n ε α µ = ε α + ε µ

2 2 3/2 2

1 ( , , ) ( , ) ( ) ( ) 3

NM e e e e e e

P n P n m α µ = α + µ µ − − ε µ π

1 (1 ) 2

p e e

n n n q n n α − = = − −

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Characteristics of charge neutral and β-stable npe- plasma

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Symmetry energy

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EOS of neutron star matter in nucleonic phase

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( ) ( )

NM QM

P P µ µ =

MFTσωρδ + MIT-bag Maxwell’s construction

Parameters of deconfinement phase transition

B - bag parameter

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Parameters of deconfinement phase transition

Q N

P ε λ ε = +

Seidov criterium

Z Seidov, Ast.Zh., 48, 443,1971

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EOS with quark deconfined phase transition

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Neutron stars with quark core TOV equations

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Neutron stars with quark core 3/ 2

cr

λ =

MeV/fm3

69,3 B ≈

MeV/fm3

69,3 B <

3/ 2 λ >

MeV/fm3 69,3 90 B ≤ ≤

3/ 2 λ ≤

MeV/fm3

90 B >

Unstable QP

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Neutron stars with quark core

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Catastrophic conversion due to deconfined phase transition

16,77 R ≈

km km

4,38

core

R ≈ 13,95 R ≈

km

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Catastrophic conversion due to deconfined phase transition

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Summary

The account of δ-meson field results in reduction of phase

transition parameters, The density jamp parameter λ , that has important significance from the point of view of infinitisimal quark core stability in neutron star, is increased.

In case of bag parameter values

the condition λ>3/2 is satisfied, and infinitisimal quark core is unstable.

For the quark phase is unstable.

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