1. From the Phys.Dept. Jan.2002Etna Double-Face, Aug.07 ISOSPIN EFFECTS on PHASE TRANSITIONS of HADRONIC to QUARK MATTER M.Colonna, V.Baran, M.Di Toro, V. Greco, Liu Bo, S. Plumari LNS-INFN and Phys.Astron.Dept. Catania, IHEP Beijing, Univ.of Bucharest …….and with the contribution of a very lively Etna mountain! NICA-Round Table, Dubna, September09, ditoro@lns.infn.it Oct.12, 2008 From the Etna Melting Pot

2. Tentative Plan of the Talk 1. Homework Symmetry Energy The problem at High Baryon Density 2. Quantum-Hadro-Dynamics: EoS Fully Covariant Transport, Essential Mean Field Effects Elliptic Isospin Flows, Meson Production 3. Transition to a Mixed Phase at High Baryon and Isospin density

3. HOMEWORK Hadron-Quark EoS at High Baryon Density Hadron : “STANDARD” EoS (with Symmetry Term) Quark: “STANDARD” MIT-Bag Model ISOSPIN EFFECTS on the MIXED PHASE Zero Temperature: two pages with a pencil….

4. EoS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings Symmetry energies hadron Quark: Fermi only symmetric neutron Gluon α s ≠0 → Softer quark EoS T=0, Gluon α s =0

5. o o x x N N Z Z kFkF Symmetric → Asymmetric Fermi (T=0) ≈ ε F /3 ~ ρ 2/3 Interaction (nucleon sector) Two-body ~ ρ, many-body correlations? Symmetry Energy a 4 term (~30MeV) of the Weiszäcker Mass Formula: at saturation E sym (Fermi) ≈ E sym (Interaction) E/A (ρ) = E(ρ) + E sym (ρ)I ² I=(N-Z)/A → search for ~ ρ γ but γ can be density dependent… → momentum dependence? neutron/proton mass splitting

6. EOS of Symmetric and Neutron Matter Dirac-Brueckner Variational+3-body(non-rel.) RMF(NL3) Density-Dependent couplings Chiral Perturbative Ch.Fuchs, H.H.Wolter, WCI Final Report EPJA 30 (2006) 5-21 symmetric AFDMC V8’+3body Fantoni et al 0807.5043 Consensus on a Stiff Symmetry Term at high density?

7.  scattering nuclear interaction from meson exchange: main channels (plus correlations)          IsoscalarIsovector Attraction & RepulsionSaturation OBE ScalarVectorScalarVector Nuclear interaction by Effective Field Theory as a covariant Density Functional Approach Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF) Relativistic structure also in isospin space ! E sym = kin. + (  vector ) – (  scalar )

8. a 4 =E sym    fixes (f   f  ) DBHF DHF f  2.0 2.5 fm2     * No  f  1.5 f  FREE f    2.5 fm 2 f  5 f  FREE Liu Bo et al., PRC65(2002)045201 RMF Symmetry Energy: the δ - mechanism 28÷36 MeV NL NLρ NLρδ Constant Coupling Expectations

9. Self-Energies: kinetic momenta and (Dirac) effective masses Upper sign: n Dirac dispersion relation: single particle energies QHD → Relativistic Mean Field Transport Equation n-rich: - Neutrons see a more repulsive vector field, increasing with f ρ and isospin density - m*(n)<m*(p) Covariance is essential → Inelastic Processes → Lorentz Force Phys.Rep.410(2005)335-466

10. RMF (RBUU) transport equation Collision term: Wigner transform ∩ Dirac + Fields Equation Relativistic Vlasov Equation + Collision Term… Non-relativistic Boltzmann-Nordheim-Vlasov drift mean field “Lorentz Force” → Vector Fields pure relativistic term

11. Au+Au 1AGeV central: Phase Space Evolution in a CM cell Testing EoS → CBM K production

12. Evidences of a STIFF Symmetry term at high baryon density Collective Flows: v 2 Flow: Large Squeeze-Out for n-rich clusters (e.g. t vs 3He at high p T ) Meson Production - π - /π + increase above the threshold - K 0 /K + yield ratio (no p T selection) FOPI data (W.Reisdorf, ECT* May 2009) at SIS energies, More to come from the LAND-CHIMERA-ALADIN Proposal at GSI

13. ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical End-Point affected? M.Di Toro, V.Greco, B.Liu, S.Plumari, NICA White Paper Contribution (2009)

14. , Exotic matter over 10 fm/c ? In a C.M. cell NPA775(2006)102-126

15. Testing deconfinement with RIB’s? (T,     ) binodal surface Hadron-RMF Quark- Bag model (two flavors)  trans onset of the mixed phase → decreases with asymmetry DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126 Mixed Phase → NLρ NLρδ GM3 1 AGeV 300 AMeV 132Sn+124Sn, semicentral B 1/4 =150 MeV

16. Mixed Phase: Boundary Shifts at Low Temperature Lower Boundary much affected by the Symmetry Energy NLρ NLρδ NL Isospin asymmetry

17. m u =m d =5.5MeV Χ=0.0 Χ=1.0 Critical End-Point for Symmetric Matter? NLρ, NL,NLρδ

18. Lower Χ=0.0 Upper Χ=1.0 Symmetric to Asymmetric (not Exotic) Matter NLρ

19. upper lower NLρδ : more repulsive high density Symmetry Energy in the hadron phase Inside the Mixed Phase (asymmetry α=0.2) Long way to reach 20% quark matter, but… lower Χ=0.5 Χ=0.2 Χ=0.5 NLρ NLρδ Dependence on the High Density Hadron EoS

20. Isospin Asymmetry in the Quark Phase: large Isospin Distillation near the Lower Border? 20% 0.2 lowerupper Signatures? Neutron migration to the quark clusters (instead of a fast emission) → Symmetry Energy in the Quark Phase? χ 1. Isospin Densities in the Two Phases

21. Χ=0.2 Χ=0.5 Χ=0.2 Χ=0.5 2. Baryon Densities in the Two Phases NLρ NLρδ Larger Baryon Density in the Quark Phase → Signatures?

22. NJL Effective Lagrangian (two flavors): non perturbative ground state with q-qbar condensation M.Buballa, Phys.Rep. 407 (2005) Gap Equation → 1 → 0 → 1/2 Large μ Large T 0 or Chiral restoration

23. M.Buballa, Phys.Rep. 407 (2005) Parameters: Λ p, G, m vs. M π, f π, (estimation) ρ B =0T=0 m u,d =5.5MeV m u,d =0.0 NJL Phase Diagram → μq→ μq

24. S.Plumari, Thesis 2009 Standard Parameters ● Coexistence ◊ Spinodal

25. Isospin Extension of the NJL Effective Lagrangian (two flavors) Mass (Gap) – Equation with two condensates α : flavor mixing parameter → α = ½, NJL, Mu=Md α → 0, small mixing, favored → physical η mass α → 1, large mixing M.Buballa, Phys.Rep. 407 (2005) Quark Dynamics at High Baryon Density

26. Neutron-rich matter at high baryon density: |Фd| decreases more rapidly due to the larger ρ d → (Ф u – Ф d ) < 0 α in the range 0.15 to 0.25……

27. Very n-rich matter: I=(N-Z)/A=0.4 Masses in the Chiral Phase α =0.2 α =1 Solutions of the Iso-Gap Equation S.Plumari, Thesis 2009 Iso-NJL m = 6MeV Λ = 590MeV G 0 Λ 2 =2.435 → M vac =400MeV =(-241.5MeV) 3 m π =140.2MeV f π =92.6MeV

29. Symmetry Energy in the Chiral Phase: something is missing ….only kinetic contribution

30. Conclusions for the Physics at NICA Isospin dependence of the Mixed Phase Signatures ( reduced v 2 at high p T, n q -scaling break down…. ) Isospin Trapping: - Reduction of n-rich cluster emission - Anomalous production of Isospin-rich hadrons at high p T - u-d mass splitting (m u >m d ) Experiments Theory Isospin effects on the spinodal decomposition Isovector Interaction in Effective QCD Lagrangians Larger Baryon Density in the Quark Phase: - Large Yield of Isospin-rich Baryons at high p T

31. Nuclear Matter Phase Diagram….NICA updated Every Complex Problem has a Simple Solution …our journey is around here ….most of the time Wrong (Umberto Eco) Conclusion:

32. Back-up Slides

33. Bag-Model EoS: Relativistic Fermi Gas (two flavors) Energy density Pressure Number density q, qbar Fermi Distributions Baryon/Isospin Densities and Chemical Potentials …only kinetic symmetry energy

34. N N-STARS: Present status with observation constraints D.Page, S.Reddy, astro-ph/0608360, Ann.Rev.Nucl.Part.Sci. 56 (2006) 327 Softer EOS→smaller R (larger ρ-central), smaller maximum Mass “The broad range of predicted radii for nucleon EOS will be narrowed in the near future owing to neutron-skin thickness and probably also to heavy-ion experiments” General Relativity AAAAAA

35. Proton fraction, y=Z/A, fixed by Esym(ρ) at high baryon density: β-equilibrium Charge neutrality, ρ e =ρ p =yρ Fast cooling: Direct URCA process Fermi momenta matching

36. Neutron Star (npeμ) properties Direct URCA threshold Mass/Radius relation NLρ NLρδ NLρ DD-F compact stars & heavy ion data T.Klaehn et al. PRC 74 (2006) 035802 - Transition to quark matter? - Faster Cooling for Heavier NS?

37. DIRAC OPTICAL POTENTIAL Dispersion relation Schrödinger mass upper signs: neutron Asymmetric Matter RMF Phys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82 ~50 MeV Dirac mass

38. BEYOND RMF: k-dependence of the Self-Energies Schroedinger mass Asymmetric Matter DBHF High momentum saturation of the optical potential High momentum increase of the Dirac Mass Phys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82 Problem still open……..sensitive observables

39. Relativistic Landau Vlasov Propagation Discretization of f(x,p*)  Test particles represented by covariant Gaussians in xp-space → Relativistic Equations of motion for x  and p*  for centroids of Gaussians Test-particle 4-velocity → Relativity: - momentum dependence always included due to the Lorentz term - E*/M* boosting of the vector contributions Collision Term: local Montecarlo Algorithm imposing an average Mean Free Path plus Pauli Blocking → in medium reduced Cross Sections C. Fuchs, H.H. Wolter, Nucl. Phys. A589 (1995) 732

40. Isospin Flows at Relativistic Energies E sym (ρ): Sensitivity to the Covariant Structure Enhancement of the Isovector-vector contribution via the Lorentz Force High p_t selections: source at higher density → Symmetry Energy at 3-4ρ 0

41. Au+Au 800 A MeV elliptic flows, semicentral Rapidity selections v2(n) |y°| < 0.5 v2(n), v2(p) vs. p_t v2(p) All rapidities v2(n) v2(p) Low p_t spectator contributions

42. Elliptic flow Difference Difference at high p t first stage approximations   0.3<Y/Y proj <0.8 132Sn+132Sn, 1.5AGeV, b=6fm: NL-  NL-(  +  High p t neutrons are emitted “earlier” Dynamical boosting of the vector contribution V.Greco et al., PLB562(2003)215 Equilibrium (ρ,δ) dynamically broken: Importance of the covariant structure

43. Hunting isospin with v 2 : the mass 3 pair A small gradual change in The difference 3 H- 3 He when Raising the beam energy for Au+Au (N/Z = 1.5) W.Reisdorf, ECT* May 09: FOPI 3H-3He V2 Results Au+Au with increasing beam energy Relativistic Lorentz effect? High p t selection CHIMERA-LAND-ALADIN Proposal at SIS-GSI and…R3B(FAIR)

44. Meson Production at Relativistic Energies:  - /  +, K 0 /K + E sym (ρ): Sensitivity to the Covariant Structure Self-energy rearrangement in the inelastic vertices with different isospin structure → large effects around the thresholds High p_t selections: source at higher density → Symmetry Energy at 3-4ρ 0

45. PION PRODUCTION Main mechanism 2. Fast neutron emission: “mean field effect” 1. C.M. energy available: “threshold effect” Vector self energy more repulsive for neutrons and more attractive for protons Some compensation in “open” systems, HIC, but “threshold effect” more effective, in particular at low energies n → p “transformation ” nn n0n0 n-n- p-p- p+p+ n  ++ n+n+ p+p+ pp p-p- π(-) enhanced π(+) reduced G.Ferini et al., NPA 762 (2005) 147, NM Box PRL 97 (2006) 202301, HIC No evidence of Chemical Equilibrium!!

46. The Threshold Effect: nn →pΔ - vs pp→nΔ ++ pp→nΔ ++ nn →pΔ - Compensation of Isospin Effects Almost same thresholds → the s in (NN) rules the relative yields → very important at low energies increase near threshold

47. Pion/Kaon production in “open” system: Au+Au 1AGeV, central Pions: large freeze-out, compensation Kaons: - early production: high density phase - isovector channel effects → but mostly coming from second step collisions… → reduced asymmetry of the source G.Ferini et al.,PRL 97 (2006) 202301 Increasing E sym Increasing E sym

48. Kaon production in “open” system: Au+Au 1AGeV, central Main Channels K 0 vs K + :opposite contribution of the δ -coupling….but second steps NN  BYK --------- N   BY   BYK  N  YK   YK

49. Au+Au central: Pi and K yield ratios vs. beam energy Pions: less sensitivity ~10%, but larger yields K-potentials: similar effects on K 0, K + Kaons: ~15% difference between DDF and NLρδ Inclusive multiplicities 132Sn+124Sn G.Ferini et al.,PRL 97 (2006) 202301 132Sn+124Sn Soft E sym stiff E sym

50. Equilibrium Pion Production : Nuclear Matter Box Results → Chemical Equilibrium Density and temperature like in Au+Au 1AGeV at max.compression (ρ~2ρ0, T~50MeV) vs. asymmetry Larger isospin effects: - no neutron escape - Δ’s in chemical equilibrium, less n-p “transformation” NPA762(2005) 147 ~ 5 (NLρ) to 10 (NLρδ) Dynamics 1.

51. Au+Au 1AGeV: density and isospin of the Kaon source n,p at High density n/p at High density Drop: Contribution of fast neutron emission and Inelastic channels: n → p transformation Time interval of Kaon production “central” density Dynamics 2.

52. Kaon ratios: comparison with experiment G. Ferini, et al., NPA 762 (2005) and PRL 97 (2006) Data (Fopi) X. Lopez, et al. (FOPI), PRC 75 (2007) Comparision to FOPI data (Ru+Ru)/(Zr+Zr) equilibrium (box) calculations finite nucleus calculations sensitivity reduced in collisions of finite nuclei single ratios more sensitive enhanced in larger systems larger asymmetries more exclusive data H.Wolter, ECT* May 09

53. Nuclear Matter Box Results Density and temperature like in Au+Au 1AGeV at max.compression vs. asymmetry Larger isospin effects: - no neutron escape - Δ’s in chemical equilibrium → less n-p “transformation” NPA762(2005) 147

54. Gas Liquid Density   Temperature 20 200 MeV Plasma of Quarks and Gluons Collisions Heavy Ion 1: nuclei 5? Phases of Nuclear Matter Philippe Chomaz artistic view Isospin ? Mixed Phase In terrestrial Labs.?

55. Lower Boundary of the Binodal Surface vs. NM Asymmetry vs. Bag-constant choice Proton-fraction symmetric NPA775(2006)102-126 α = 1-2 Z/A