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

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

Introduction RMF-theory: J.D.Walecka, Ann.Phys. 87, 4951, 1974 σ ω ρ B.D.Serot, J.D.Walecka, Int.J.Mod.Phys. E6, 515, 1997 . Low density asymmetric nuclear matter: S.Kubis, M.Kutschera , Phys. Lett., B399,191,1997. σ ω ρ δ B.Liu, V.Greco, V.Baran, M.Colonna, M.Di Toro , Phys. Rev. C65, 045201, 2002. Heavy ion collisions at intermediate energies: V.Greco, M.Colonna, M.Di Toro, F.Matera , Phys. Rev. C67, 015203, 2003 σ ω ρ δ V.Greco et al., Phys. Lett. B562, 215, 2003. T.Gaitanos, M.Colonna, M.Di Toro, H.H.Wolter, Phys.Lett. B595, 209,2004. Neutron stars without quark deconfinement: . σ ω ρ δ B.Liu, H.Guo, M.Di Toro, V.Greco , arXiv Nucl-th/0409014 v2, 2005

Lagrangian density of many-particle system of p,n. σ , ω , ρ , δ � ⎡ ⎤ ⎛ ⎞ � � ( � ) 1 µ = ψ γ ∂ − ω − τ ⋅ ρ − − σ − τ ⋅ δ ψ + L ⎢ ⎜ ( ) ( ) ⎟ ( ) ( ) ⎥ i g x g x m g x g x µ ω µ ρ µ σ δ N N N N N ⎝ ⎠ ⎣ ⎦ 2 ( ) 1 1 1 µ µ µν + ∂ σ ∂ σ − σ − σ + ω ω − Ω Ω + 2 2 2 ( ) ( ) ( ) ( ( )) ( ) ( ) ( ) ( ) x x m x U x m x x x x µ σ ω µ µν 2 2 4 � � � ( ) � � 1 1 1 µ µ µν + ∂ δ ∂ δ − δ + ρ ρ − 2 2 2 ( ) x ( ) x m ( ) x m ( ) x ( ) x R ( ) x R ( ) , x µ δ ρ µ µν 2 2 4 ψ � ⎛ ⎞ � = = σ ω δ ρ ψ = ⎜ p ⎟ x x ( , , , ) t x y z ( ), x ( ), x ( ), x ( ) x µ µ µ N ψ ⎝ ⎠ n b c σ = σ + σ 3 4 U ( ) m ( g ) ( g ) , σ σ Scalar Vector N 3 4 σ ω Isoscalar Ω = ∂ ω −∂ ω ( ) x ( ) x ( ), x µν µ ν ν µ δ ρ ℜ = ∂ ρ −∂ ρ Isovector ( ) x ( ) x ( ). x µν µ ν ν µ

Relativistic mean-field approach ∂ ∂ L L − ∂ = 0 µ ∂ φ ∂ ∂ φ ( ) x ( ( )) x µ = − σ − δ * (3) m m g g , σ δ p N 1 = + + ω + ρ 2 * 2 (3) e ( ) k k m g g , = − σ + δ ω ρ * (3) . m m g g p p 0 0 2 σ δ n N 1 = + + ω − ρ 2 * 2 (3) e ( ) k k m g g , ω ρ n n 0 0 2 3 3 k k = = Fp Fn n , n , π π σ p n 2 2 ⎛ ⎞ 3 3 dU ( ) , σ = + − 2 ⎜ ⎟ m g n n σ σ σ s p sn ⎝ ⎠ k * d F p m 1 ∫ = π p 2 n k dk , s p 2 ( ) + 2 * 2 k m ω = + 2 0 m g n n , p ω ω p n k * ( ) F n m 1 ∫ δ = − = π 2 (3) n 2 m g n n , n k dk . δ δ s p sn sn 2 + 2 * 2 k m 0 n ( ) 1 ρ = − 2 (3) m g n n , ρ ρ 0 p n 2 1 µ = = + + ω + ρ 2 * 2 (3) e ( k ) k m g g , ω ρ p p F p F p p 0 0 2 1 µ = = + + ω − ρ 2 * 2 (3) e ( k ) k m g g . ω ρ n n F n F n n 0 0 2

Parametric EOS for nuclear matter σ ≡ σ ω ≡ ω δ ≡ δ ρ ≡ ρ (3) (3) g , g , g , g , σ ω δ ρ 0 2 2 2 2 ⎛ ⎞ − ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ g n n g g g ρ σ ≡ ω ≡ δ ≡ ≡ α = the asymmetry parameter ⎜ ⎟ n p ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ a , a , a , a , ⎜ ⎟ σ ω δ ρ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ m m m m ⎝ ⎠ n σ ω δ ρ 13 −α k ( )(1 n ) ⎛ ⎞ F 1 2 ∫ α = − α + − σ − δ − + − σ − δ + 2 2 2 2 2 P n ( , ) ⎜ k ( ) (1 n ) 3 ( m ) k ( m ) ⎟ k dk π F N N 2 ⎝ ⎠ 0 13 +α k ( )(1 n ) ⎛ ⎞ F 1 2 ∫ + + α + − σ + δ − + − σ + δ − 2 2 2 2 2 ⎜ k ( ) (1 n ) 3 ( m ) k ( m ) ⎟ k dk π F N N 2 ⎝ ⎠ 0 ⎛ ⎞ σ ω δ ρ 2 2 2 2 1 � − σ + − + − + ⎜ ⎟ U ( ) . ⎜ ⎟ 2 a a a a ⎝ ⎠ σ ω δ ρ 13 −α k ( )(1 n ) F 1 ∫ ε α = + − σ − δ + 2 2 2 ( , ) ( ) n k m k dk π N 2 0 13 +α ⎛ ⎞ k ( )(1 n ) σ ω δ ρ 2 2 2 2 F 1 1 ∫ � + + − σ + δ + σ + + + + ⎜ ⎟ 2 2 2 k ( m ) k dk U ( ) , ⎜ ⎟ π N 2 2 a a a a ⎝ ⎠ σ ω δ ρ 0

Parameters of RMF theory a , a , a , a , b c , σ ω δ ρ α = = Symmetric nuclear matter Saturation density ( 0 ) ( n n ) 0 = γ σ = − γ * m m , (1 ) m N N 0 N ε α ε d ( , ) n ( n ,0) B = = + = Binding energy per baryon 0 m f , f , N 0 0 dn = n A n n 0 0 α= 0 ) ( 1 ω = + − + − σ 2 2 a m f k ( n ) ( m ) N 0 F 0 N 0 n 0 ω = = + − + −σ 2 2 a n m f k ( n ) ( m ) ω 0 0 N 0 F 0 N 0 k ( n ) σ − σ F 0 2 ( m ) ∫ = − σ − σ 2 2 3 0 0 N k dk bm c π N 0 0 2 + − σ a 2 2 k ( m ) σ 0 N 0

Parameters of RMF theory k ( n ) ⎛ ⎞ σ 2 F 0 2 b c 1 ∫ ε = + = + − σ + σ + σ + + 2 2 2 3 4 2 ⎜ 0 ⎟ n m ( f ) k ( m ) k dk m n a ω π 0 0 N 0 N 0 N 0 0 0 2 ⎝ ⎠ 3 4 2 a σ 0 ε α 2 d ( , ) n = compressibility module 2 9 ( ) K n 0 2 dn n = n n 0 α= 0 ε ε α 2 1 d ( , ) n = α = sym 2 E ( ) n E ( ) n α sym sym 2 2 n d n α= 0 Symmetry energy = m 938,93 MeV N fm − = 3 n 0,153 0 * m γ = = N 0,78 m 2 2 a a fm fm 0 0 0,5 0,5 1 1 1,5 1,5 2 2 2.5 2.5 3 3 N δ δ = K 300 MeV = − 2 2 4,794 4,794 6,569 6,569 8,340 8,340 10,104 10,104 11,865 11,865 13,621 13,621 15,372 15,372 f 16,3 MeV a a fm fm 0 ρ ρ = (0) E 32,5 MeV sym

Parameters of RMF theory σωρ σωρδ Parameters a σ , fm 2 9.154 9.154 a ω , fm 2 4.828 4.828 a δ , fm 2 0 2.5 a ρ , fm 2 4.794 13.621 b , fm -1 1.654 10 -2 1.654 10 -2 c 1.319 10 -2 1.319 10 -2

Properties of asymmetric nuclear matter

Properties of asymmetric nuclear matter

Characteristics of β -equilibrium npe- plasma ε α µ = ε α + ε µ ( , , n ) ( , ) n ( ), NM e e e 1 α µ = α + µ µ − − ε µ 2 2 3/2 P ( , , n ) P n ( , ) ( m ) ( ) π NM e e e e e e 2 3 − n n 1 (1 n = = − α − p e e q ) n 2 n

Characteristics of charge neutral and β -stable npe- plasma

Symmetry energy

EOS of neutron star matter in nucleonic phase

Parameters of deconfinement phase transition MFT σωρδ + MIT-bag µ = µ ( P ) ( P ) NM 0 QM 0 Maxwell’s construction B - bag parameter

Parameters of deconfinement phase transition ε λ = Q ε + P N 0 Seidov criterium Z Seidov, Ast.Zh., 48, 443,1971

EOS with quark deconfined phase transition

Neutron stars with quark core TOV equations

Neutron stars with quark core B < λ > MeV/fm 3 69,3 3/ 2 B ≈ λ = MeV/fm 3 69,3 3/ 2 cr λ ≤ ≤ ≤ MeV/fm 3 3/ 2 69,3 B 90 B > MeV/fm 3 Unstable QP 90

Neutron stars with quark core

Catastrophic conversion due to deconfined phase transition ≈ km R 4,38 core R ≈ km 16,77 R ≈ km 13,95

Catastrophic conversion due to deconfined phase transition

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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