Exploring the Isovector Equation of State at High Densities with HIC

INT program Interfaces between structure and reactions for rare isotopes and nuclear astrophysics Seattle, August 8 - September 2, 2011

Exploring the isovector equation of state at high densities with HIC

Vaia D. Prassa

Aristotle University of Thessaloniki Department of Physics Introduction Quantum Hadrodynamics (QHD) Transport theory Particle Production Summary & Outlook Outline

1 Introduction Nuclear Equation of state Symmetry Energy Phase diagram Spacetime evolution

2 Quantum Hadrodynamics (QHD) Meson exchange model Asymmetric Nuclear Equation of State

3 Transport theory Vlasov term Collision term

4 Particle Production Cross sections Kaon-nucleon potential

5 Summary & Outlook

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 2 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook First questions to be answered: Why is the Symmetry Energy so important? At low densities: Nuclear structure (neutron skins, pigmy resonances), Nuclear Reactions (neutron distillation in fragmentation, charge equilibration), and Astrophysics, (neutron star formation, and crust), At high densities: Relativistic Heavy ion collisions (isospin flows, particle production), Compact stars (neutron star structure), and for fundamental properties of strong interacting systems (transition to new phases of the matter). Why HIC? Probing the in-medium nuclear interaction in regions away from saturation. Reaction observables sensitive to the symmetry term of the nuclear equation of state. High density symmetry term probed from isospin effects on heavy ion reactions at relativistic energies. In this talk: HIC at intermediate energies 400AMeV -2AGeV . Investigation of particle ratios: Probes for the symmetry energy density dependence. In-medium effects in inelastic cross sections & Kaon potential choices.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 3 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook First questions to be answered: Why is the Symmetry Energy so important? At low densities: Nuclear structure (neutron skins, pigmy resonances), Nuclear Reactions (neutron distillation in fragmentation, charge equilibration), and Astrophysics, (neutron star formation, and crust), At high densities: Relativistic Heavy ion collisions (isospin flows, particle production), Compact stars (neutron star structure), and for fundamental properties of strong interacting systems (transition to new phases of the matter). Why HIC? Probing the in-medium nuclear interaction in regions away from saturation. Reaction observables sensitive to the symmetry term of the nuclear equation of state. High density symmetry term probed from isospin effects on heavy ion reactions at relativistic energies. In this talk: HIC at intermediate energies 400AMeV -2AGeV . Investigation of particle ratios: Probes for the symmetry energy density dependence. In-medium effects in inelastic cross sections & Kaon potential choices.

Equation of State (EOS) The nuclear matter thermodynamical properties are described by an equation of state.

The nuclear EOS gives the binding energy E/A or the pressure P of the system per nucleon, as a function of the baryon density or the temperature.

E(ρ, T ) = Eth(ρ, T )+ Ec (ρ, T = 0)+ E0

Eth(ρ, T ): thermic energy, consists of a kinetic and a dynamic term. Ec (ρ, T = 0): compression energy at T = 0. E0: binding energy at T = 0 and ρ0.

2 ∂2E Incompressibility: K = 9ρ0( 2 )|ρB =ρ0 ∂ρB

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 4 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook

Equation of State (EOS) The nuclear matter thermodynamical properties are described by an equation of state.

The nuclear EOS gives the binding energy E/A or the pressure P of the system per nucleon, as a function of the baryon density or the temperature.

E(ρ, T ) = Eth(ρ, T )+ Ec (ρ, T = 0)+ E0

Eth(ρ, T ): thermic energy, consists of a kinetic and a dynamic term. At ρsat : well deﬁned by studies on stable nuclei. Ec (ρ, T = 0): compression energy at T = 0. E0: binding energy at T = 0 and ρ0. High ρB : is predicted by the theoretical models 2 ∂2E and is adjusted to ﬁt the HIC data. Incompressibility: K = 9ρ0( 2 )|ρB =ρ0 ∂ρB Constraints from HIC: Multiplicities and Flows of n and p .

Symmetry Energy The EOS depends on the asymmetry parame- N−Z ter α = N+Z :

(ρB ,α) 2 E(ρB , α) ≡ = E(ρB , 0) + Esym(ρB )α ρB Thus, it gives a deﬁnition of the symmetry energy:

1 ∂2E(ρ , α) 1 ∂2 E ≡ B | = ρ | sym 2 α=0 B 2 ρB3=0 2 ∂α 2 ∂ρB3

2 2 ∂ Esym Ksym = 9ρ0( 2 )|ρB =ρ0 ∂ρB The symmetry energy describes the diﬀerence between the binding energy of the symmetric matter and that of the pure neutron matter.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 5 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook

Symmetry Energy The EOS depends on the asymmetry parame- N−Z ter α = N+Z :

(ρB ,α) 2 E(ρB , α) ≡ = E(ρB , 0) + Esym(ρB )α ρB Thus, it gives a deﬁnition of the symmetry energy:

1 ∂2E(ρ , α) 1 ∂2 E ≡ B | = ρ | sym 2 α=0 B 2 ρB3=0 2 ∂α 2 ∂ρB3

2 Different behavior even at saturation point. 2 ∂ Esym Ksym = 9ρ0( 2 )|ρB =ρ0 ∂ρB High ρB , discrepancies between the models The symmetry energy describes the difference increases. between the binding energy of the symmetric matter and that of the pure neutron matter. Constraints from HIC: Multiplicities and Differential flows of n and p. Pion flows and Isospin ratios π−/π+, K 0/K + .

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 6 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook

Liquid phase: T ≈ 10MeV .

Gas phase: RHIC T ≈ 10 − 100MeV . Liquid phase: T ≈ 10MeV .

Quark-gluon plasma: Ultra RHIC T > 100MeV Gas phase: RHIC T ≈ 10 − 100MeV . Liquid phase: T ≈ 10MeV .

Initial stage. Nuclei at ground state. P = 0, T = 0, ρ = ρ0.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 7 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook

Compression. Sequential N-N binary collisions. Incoming matter of the target & the projectile is mixed & compressed forming a short-lived stage of nuclear matter of high ρB that depends on the EOS. E = 1AGeV , T ≈ 30 − 60MeV , ρB ≈ 2 − 3ρ0. Initial stage. Nuclei at ground state. P = 0, T = 0, ρ = ρ0.

Expansion. Expansion of the density energy. T , ρ ⇓. Hot matter interacts with the cold matter of the spectator. Ebeam > 10AGeV ⇒ QGPlimit , P lower than Phadronic phase . Compression. Sequential N-N binary collisions. Incoming matter of the target & the projectile is mixed & compressed forming a short-lived stage of nuclear matter of high ρB that depends on the EOS. E = 1AGeV , T ≈ 30 − 60MeV , ρB ≈ 2 − 3ρ0. Initial stage. Nuclei at ground state. P = 0, T = 0, ρ = ρ0.

Freeze-out. Low ρB ⇒ no further interaction. Expansion. Expansion of the density energy. T , ρ ⇓. Hot matter interacts with the cold matter of the spectator. Ebeam > 10AGeV ⇒ QGPlimit , P lower than Phadronic phase . Compression. Sequential N-N binary collisions. Incoming matter of the target & the projectile is mixed & compressed forming a short-lived stage of nuclear matter of high ρB that depends on the EOS. E = 1AGeV , T ≈ 30 − 60MeV , ρB ≈ 2 − 3ρ0. Initial stage. Nuclei at ground state. P = 0, T = 0, ρ = ρ0.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 7 Introduction Quantum Hadrodynamics (QHD) Meson exchange model Transport theory Asymmetric Nuclear Equation of State Particle Production Summary & Outlook

The NN Interaction is described by the exchange of mesons. SCALAR (attraction): σ, δ (isospin dependence). VECTOR (repulsion): ω, ρ (isospin dependence).

Lagrangian density

¯ µ 1 µ 1 2 µ 1 µν L = ψ(iγ ∂µ − m)ψ + 2 ∂µσ∂ σ − U(σ) + 2 mωωµω − 4 Ωµν Ω

1 2 ~µ 1 ~ ~ µν 1 ~ µ~ 2 ~2 + 2 mρ~ρµ · ρ − 4 Rµν R + 2 (∂µδ · ∂ δ − mδδ ) ¯ ~ + ψ(−gωωµ − gργ~τ · ~ρµ + gσσ + gδ~τ · δ)ψ

1 2 2 1 3 Lagrangian density of: the free nucleons, the σ meson with U(σ) = 2 mσσ + 3 g2σ + 1 4 4 g3σ , the ω meson with the ﬁeld tensor Ωµν ≡ ∂µων − ∂ν ωµ, the ρ meson with the ﬁeld tensor R~ µν ≡ ∂µ ~ρν − ∂ν ~ρµ, the δ meson and of their interaction.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 8 Introduction Quantum Hadrodynamics (QHD) Meson exchange model Transport theory Asymmetric Nuclear Equation of State Particle Production Summary & Outlook The nuclear EOS for asymmetric nuclear matter in the QHD picture: Z 3 X d k ? 1 2 1 2 1 2 E = 2 E (k) + U(Φ) + f ρ + fρρ + f ρ (2π)3 i 2 V B 2 B3 2 δ S3 i=n,p The nuclear Symmetry energy in the QHD picture :

2 23 2 ∗ ! 1 kF 1 m Esym = ∗ + 4fρ − fδ ∗ 5 ρB 6 EF 2 EF

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 9 Introduction Quantum Hadrodynamics (QHD) Vlasov term Transport theory Collision term Particle Production Summary & Outlook Relativistic transport equation Relativistic Boltzmann-Uehling-Uhlenbeck (RBUU)

∗ µ ∗ µν ∗ µ ∗ p∗ ∗ [pµi ∂x + gωpνi Fi + mi (∂x mi ) ∂µ ]fi (x, p )= 3 ∗ 3 ∗ 3 ∗ g R d p2 d p3 d p4 ∗ ∗ ∗ ∗ 3 ∗0 ∗0 ∗0 W (p , p2, p3, p4) (2π) p2 p3 p4 {f3f4[1 − f ][1 − f2] − ﬀ2[1 − f3][1 − f4]}

Vlasov term. Temporal evolution of the system, which is described by the phase-space distribution function f (x, p∗), under the influence of a mean field ∗ ∗ (mi , pi ). Collision term. Transition rate W , is expressed by the differential cross section dσ ( dΩ(s,Θ) ),

dσ W (p∗, p∗, p∗, p∗) = (p∗ + p∗)2 δ4(p∗ + p∗ − p∗ − p∗) 2 3 4 2 dΩ 2 3 4 where Θ is the scattering angle in the cms frame and s the square of the total ∗ ∗ 2 energy, s = (p + p2 ) .

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 10 Introduction Quantum Hadrodynamics (QHD) Vlasov term Transport theory Collision term Particle Production Summary & Outlook

Test particle method Representation of the phase-space distribution function by a number of test particles.

Gaussian test particles

∗ ∗ 2 2 ∗ ∗ (p −pi (τ)) /σp ˆ ∗ ∗µ ∗2˜ g (p − pi (τ)) = αp e δ pµpi (τ) − mi

Distribution function

∗ 1 A·N +∞ R (x)Rµ(x)/σ2 (p∗−p∗(τ))2/σ2 f (x, p ) = P R dτ e iµ i e i p N(πσσp ) i=1 −∞ µ ˆ ∗ ∗µ ∗2˜ ×δ[(xµ − xiµ(τ))ui (τ)]δ pµpi (τ) − mi

Test particles equations of motions

∗ d µ pi (τ) xi = ∗ , dτ mi (xi ) ∗ d ∗µ piν (τ) µν µ ∗ pi = ∗ Fi (xi (τ)) + ∂ mi (xi ) dτ mi (xi )

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 11 Introduction Quantum Hadrodynamics (QHD) Vlasov term Transport theory Collision term Particle Production Summary & Outlook

Collision term Inelastic channels 3 ∗ 3 ∗ 3 ∗ I = g R d p2 d p3 d p4 W (p∗, p∗, p∗, p∗) c (2π)3 p∗0 p∗0 p∗0 2 3 4 Ingoing Outgoing Isospin 2 3 4 channel Channel coeﬃcients {f (x, p∗)f (x, p∗)[1 − f (x, p∗)][1 − f (x, p∗)] − 3 4 2 − ∗ ∗ ∗ ∗ nn p∆ 1 f (x, p )f (x, p2 )[1 − f (x, p3 )][1 − f (x, p4 )]} n∆0 2/3 np p∆0 1/3 n∆+ 2/3 ∗ pp p∆+ 1/3 Factors (1 − fi ), (fi = f (x, pi )), Pauli principle. n∆++ 1 Transition rate: Decay width: 4 4 ∗ 4 2 W = (2π) δ (k + k2 − k3 − k4)(m ) |T | . q3R2 q2 + δ2 Two particles collide if: Γ(q) = Γ˜ z(q), z(q) = r 2 2 2 2 q σtot 1 + q R q + δ d < d0 = π .

Elastic channels Resonance decay probability P, 1 NN ⇐⇒ NN » Γ(M)∆t – P = 1 − exp − 2 N∆ ⇐⇒ N∆ γ~c 3 ∆∆ ⇐⇒ ∆∆

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 12 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Elastic Baryon-Baryon collisions In-medium eﬀects: Dirac-Brueckner.

Suppression of cross sections at Ebeam < 300AMeV and high ρB .

At high Elab, the σeﬀ approaches asymp- totically σfree

Fuchs et al. Phys. Rev. C64 (2001), 024003.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 13 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Inelastic Baryon-Baryon collisions In-medium eﬀects: DBHF. Ter Haar and Malﬂiet, Phys.Rev.C36, 4 (1987)

inel inel σeﬀ = f (ρ)σfree (Elab)

2 f (ρ) = 1 + a0(ρB /ρ0) + a1(ρB /ρ0) + 3 a2(ρB /ρ0) . Inverse channel: 2 (2SN +1)(2SN +1) qf σN∆→NN = (2S +1)(2S +1) 2 σNN→N∆. N ∆ qi

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 14 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

State I3 Decay channel Weights ∆− −3/2 nπ− 1 ∆0 −1/2 pπ− 1/3 nπ0 2/3 ∆+ +1/2 p π0 2/3 n π+ 1/3 ∆++ +3/2 p π+ 1

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 15 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

20 20

"eff "free # ! (FOPI) # + ! (FOPI) ! 15 15 Centrality dependence +,- ! 10 10 Au + Au collision at 1AGeV . M ! ! Apart : number of participants in a collision.

5 5 Overestimation of data.

0 0 0.0 100.0 200.0 300.0 400.0 Apart

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 16 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

20 20

"eff "free # ! (FOPI) # + ! (FOPI) ! 15 15 Centrality dependence +,- ! 10 10 Au + Au collision at 1AGeV . M ! ! Apart : number of participants in a collision.

5 5 Overestimation of data.

0 0 0.0 100.0 200.0 300.0 400.0 Apart

Transverse momentum spectra Au + Au collision at 1AGeV , at mid-rapidity (−0.2 < y 0 < 0.2).

Very good agreement with data.

4 FOPI 2 ! # + free " " !eff 1.75

3 1.5 Pion rapidity distribution 1.25

Au + Au collision at Ebeam = 1 AGeV , (0) 2 1 with pt > 0.1 GeV /c. dN/dy 0.75 Mid rapidity region: good agreement. 1 0.5

Spectator region: overestimation. 0.25

0 0 -2 -1 0 1 2 -2 -1 0 1 2 (0) (0) y y

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 17 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Nπ YK N∆ BYK 0.04 0.04

Kaon production 0.03 0.03

0.02 0.02 yields 1 0

πB −→ YK K σ 0.01 eff 0.01 σ 2 BB −→ BYK free 0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Au + Au central collision at 1AGeV . 0.03 0.03

0.02 0.02 yields +

K 0.01 0.01

0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 time (fm/c) time (fm/c)

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 18 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Nπ YK N∆ BYK 0.04 0.04

Kaon production 0.03 0.03

0.02 0.02 yields 1 0

πB −→ YK K σ 0.01 eff 0.01 σ 2 BB −→ BYK free 0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Au + Au central collision at 1AGeV . 0.03 0.03

0.02 0.02 yields +

K 0.01 0.01

0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 time (fm/c) time (fm/c) w/o K-pot

σfree σeff + FOPI Rapidity distribution of K KaoS 0.1 Ni + Ni collision at 1.93AGeV . (0) +

σeﬀ : reduction of K =⇒ towards a dN/dy better agreement with data. 0.05

0 -1 0 1 (0) y Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 18 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Yield ratios: Determination of the Esym behavior.

π−/π+: partially aﬀected from the in-medium cross sections. K 0/K +: appears robust against the in-medium cross sections.

V. Prassa et al, Nucl.Phys. A789, 311-333 (2007)

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 19 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Kaons equation of motion Kaon in-medium energy

ˆ µ 2 ∗2˜ (∂ + iVµ) + mK φK (x) = 0 q 2 ∗2 EK (k) = k0 = k + mK + V0 Chiral perturbation theory potential 3 V = j µ ∗2 µ NL 8fπ ChPT s Σ m∗ = m2 − KN ρ + V V µ K K 2 s µ fπ K 1.2 OBE (k=0)/m K

One boson exchange model potential E

1 V µ = f ∗jµ 3 ω r 1 ∗ 2 mK mK = m + gσN σ K 3 0 1 2 3 4 ρΒ/ρ0

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 20 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Kaons equation of motion Kaon in-medium energy

ˆ µ 2 ∗2˜ (∂ + iVµ) + mK φK (x) = 0 q 2 ∗2 EK (k) = k0 = k + m + V0 Chiral perturbation theory potential K 3 1 Vµ = jµ± j 0 ∗2 ∗2 µ3 K 8fπ 8fπ NL ChPT s NLρ ∗ ΣKN C + m = m2 − ρ + V V µ∓ ρ K K K 2 s µ 2 s3 fπ fπ

0 K K 1.2 OBE One boson exchange model potential (k=0)/m

K + E K

µ 1 ` ∗ µ µ´ V = f j ±fρj 3 ω 3 r m m∗ = m2 + K g σ 1 K K 3 σN 0 1 2 3 4 ρΒ/ρ0 upper sign K +

Kaons equation of motion Kaon in-medium energy

ˆ µ 2 ∗2˜ (∂ + iVµ) + mK φK (x) = 0 q 2 ∗2 EK (k) = k0 = k + m + V0 Chiral perturbation theory potential K 3 1 Vµ = jµ± j 0 ∗2 ∗2 µ3 K 8fπ 8fπ NL NLρ ChPT s NLρδ ∗ ΣKN C + m = m2 − ρ + V V µ∓ ρ K K K 2 s µ 2 s3 fπ fπ

0 K K 1.2 OBE One boson exchange model potential (k=0)/m

K + E K

µ 1 ` ∗ µ µ´ V = f j ±fρj 3 ω 3 r m m∗ = m2 + K (g σ∓f ρ ) 1 K K 3 σN δ S3 0 1 2 3 4 ρΒ/ρ0 upper sign K +

Rapidity distribution: Dependence on the VK Central Au + Au@1AGeV . Reduction in the whole rapidity region. OBE: less stopping.

Combination of VK and σeﬀ : further reduction.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 21 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Rapidity distribution: Dependence on the VK Central Au + Au@1AGeV . Reduction in the whole rapidity region. OBE: less stopping.

Combination of VK and σeﬀ : further reduction.

Rapidity distribution: Isospin dependent-VK Central Au + Au@1AGeV .

Rapidity distributions not aﬀected. Main contribution: mid-rapidity region.

Combination VK and σeﬀ : further reduction.

Rapidity distributions of K + Ni + [email protected] b < 4fm. ChPT: σfree good agreement with exp. data. σeﬀ : underestimation of the exp. data. OBE: σfree good agreement with exp. data. σeﬀ : on the exp. data.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 22 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Centrality dependence K + Au + Au@1AGeV collision.

Underestimation of the experimental data. OBE: closer to the exp.data.

V. Prassa et al, Nucl.Phys. A832 88-99 (2010)

Temporal evolution of K 0/K + Central Au + Au@1AGeV . OBE: reduction K 0/K +. Favors K + production. ChPT: raise. Favors K 0 production.

IOBE: raise K 0/K +. IChPT: sharp drop.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 23 Introduction Quantum Hadrodynamics (QHD) Cross sections Transport theory Kaon-nucleon potential Particle Production Summary & Outlook

Temporal evolution of K 0/K + Central Au + Au@1AGeV . OBE: reduction K 0/K +. Favors K + production. ChPT: raise. Favors K 0 production.

IOBE: raise K 0/K +. IChPT: sharp drop.

K 0/K + dependence on the EOS Central Au + Au@1AGeV .

IChPT: reduction ≈ 20%.

IOBE: NLρ ≈ 3%, while NLρδ ≈ 5%.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 23 Introduction Quantum Hadrodynamics (QHD) Transport theory Particle Production Summary & Outlook Summary Effective N-N cross sections: Dirac Brueckner Hartree Fock. Pions: reduction of production. At mid-rapidity good agreement with the data. π−/π+: depends on the effective inelastic cross sections. Kaons: more affected (≈ 30%). K 0/K + almost unchanged (large mean free path). Kaon-nucleon potential 1 Chiral Perturbation Theory, ChPT. 2 One-Boson-Exchange, OBE. Reduction of kaon production. Good agreement with the data (particularly with OBE). ChPT: K 0/K + depends on the parametrization of the EOS. OBE: K 0/K + more robust against the EOS parametrization. Outlook Inclusion of momentum dependence. T. Gaitanos, et al. Nucl.Phys. A828, 9-28 (2009). Improvement of NN-interactions.

Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 24 THANK YOU FOR YOUR ATTENTION Collaborations:

M. Di Toro, M. Colonna LNS, Catania

H. H. Wolter LMU, Muenchen

Theo Gaitanos U. Giessen

G. A. Lalazissis U. Thessaloniki

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