1. Search for Simmetry Energy at high density V. Greco on Behalf of the Theory Group of Catania University of Catania INFN-LNS

2. Outline  Symmetry energy at high density, E≥400 AMeV:  relativistic structure of E sym  n/p, 3 H/ 3 He ratio & flows (impact of m* n,p )  particle production (    , K 0 /K + )  Dependence of QGP transition on isospin  Strong isospin fractionation (large asymmetry in the quark phase) - implementation in the transport codes -> signatures - implementation in the transport codes -> signatures

3. Symmetry Energy High density/energy Probes n/p and LCP ratios p/n differential flow pions flow and ratios kaon ratios neutron stars …. Liquid drop model How the value depends on density,.i.e. -> EOS for any n,p content Theoretical predictions Only Stiff- Soft is not predicted! V. Greco et al., PRC63(01)-RMF-HF

4.   model Only kinetic contribution to E sym  Charged mesons : (scalar isovector) (vector-isovector) Splitting n & p M * Relativistic structure also in isospin space ! E sym = cin. + (  vector ) – (  scalar ) Isospin degrees of freedom in QHD QHD-II QHD-II QHD-I QHD-I The Dirac equation becomes: meson-like fields exchange model

5. a 4 =E sym    fixes (f   f  ) Similar structure in DBHF, DHF, DDC, PC-RMF, … consistent with large fields observed in lQCD f  2.0 2.5 fm 2     * No  f  1.5 f  FREE 15 MeV f    2.5 fm 2 f  5f  FREE (50-35) MeV F. Hoffmann et al., PRC64 (2001) 034314 V. Greco et al., PRC63(2001)035202 Symmetry Energy in RMFT (~DBHF) Balance of isospin fields of ~ 100 MeV B.Liu, PRC65(01)045201

6. Lane potential Important for: nucleon emission, flow, particle production      data m* n < m* p m* n > m* p Momentum dependence Gives a different contribution at equilibrium but in HIC E sym pot (r,k) -> m* p, ≠ m* n RMFT-SkLya opposite behavior, but there are several sources of MD… Mean Field Symmetry energy

7. Non-relativistic mass Parametrize non-locality in space & time Dirac mass (for Rel.Mod.) C. Fuchs, H.H. Wolter, EPJA 30(2006)5 Effective masses: different definitions The real issue with RMFT is not the Dirac or the non-relativistic, but the zero range approximation that means an explicit MD contribution is missed Diffence in proton/neutron effective masses Dirac-RMFT

8. ISOSPIN EMISSION & COLLECTIVE FLOWS: - Checking the n,p splitting of effective masses High p T selections: - source at higher density - squeeze-out

9. asy-stiff asy-soft Light isobar 3 H/ 3 He yields Mass splitting: N/Z of Fast Nucleon Emission Observable very sensitive at high p T to the mass splitting and not to the asy-stiffness 197 Au+ 197 Au 600 AMeV b=5 fm, y(0)  0.3 (squeeze-out) m* n >m* p m* n <m* p V.Giordano, ECT* May 09 asy-stiff asy-soft Crossing of the symmetry potentials for a matter at ρ≈1.7ρ 0 n/p ratio yields

10. m* n <m* p : larger neutron squeeze out at mid-rapidity - Larger neutron repulsion for asy-stiff Mass splitting impact on Elliptic Flow m*n < m*p m*n > m*p 197 Au+ 197 Au, 400 AMeV, b=5 fm, y (0)  0.5 v 2 vs rapidity for 3 H and 3 He: Larger flow but less isospin effects v 2 vs p T V.Giordano, ECT* May 09 Increasing relevance of isospin effects for m* n <m* p m* n >m* p m* n <m* p v 2 vs Y/Y 0

11. Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF) Covariant Mean Field Dynamics Phys.Rep.410(2005)335-466 Relativistic Energies

12. RBUU transport equation Elastic Collision term Wigner transform ∩ Dirac + Fields Equation Relativistic Vlasov Equation + Collision Term… Non-relativistic BNV “Lorentz Force” → Vector Fields pure relativistic term Upper sign: n Single particle energies n-rich: - Neutrons see a more repulsive vector field, increasing with f ρ and isospin density - m*n<m*p

13. Dynamical Effect of Relativistic Structure approximations   0.3<Y/Y proj <0.8 132 Sn+ 132 Sn, 1.5AGeV, b=6fm Dynamical boosting of the Isopin effect that is larger when f  is larger V.Greco et al., PLB562(2003)215 Equilibrium (ρ,δ) dynamically broken: Importance of the covariant structure f , f  determined from   p-n v 2 flow V. Greco et al. PLB562 (2003)

14. 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 3 H- 3 He V 2 Results Au+Au with increasing beam energy Relativistic Lorentz effect? The vector part of the isovector gets dynamically enhanced at E~1.5 AGeV (V. Greco et al. PLB562 (2003)) Hunting isospin with v 2 : the mass 3 pair

15. PARTICLE PRODUCTION with different ISOSPIN: -  - /  + vs K - /K 0 - Circumstantial reasons to be careful - more theorethical efforts …

16. Pion vs Kaon as a measure of EOS In the 80’s there was the idea of using pions to infer the EOS C.M. Ko & J. Aichelin, PRL55(85)2661 pointed out that kaons provide a more sensitive and more clean probe of high density EOS. No conclusion on EOS from pion production C. Fuchs, Prog.Part. Nucl. Phys. 56 (06) - Pions produced and absorbed during the entire evolution of HIC - Kaons are closer to threshold -> come only from high density - Kaons have large mean free path -> no rescattering & absorption - Kaons small width -> on-shell Bao An Li and L.W. Chen group shows that the situation is less drammatic that the envisaged one for      E sym ~20 years after

17. Kaons: - direct early production: high density phase - isovector channel effects Au+Au@1AGeV  /K production in “open” system: Au+Au 1AGeV, central Production stopped at the maximum of the  ’s production ~15 fm/c, K’s purely coming from maximum density Not affected by  rescatterng absorption

18. ISOSPIN EFFECTS ON PION PRODUCTION Main mechanism 1. Fast neutron emission: “mean field effect” (Bao-An) 2. C.M. energy available: “threshold effect” (Di Toro) Vector self energy + for n and - for p n → p “transformation” nn n0n0 n-n- p-p- p+p+ n  ++ n+n+ p+p+ pp p-p- Dominant close to sub-threshold 3. Isospin  -hole exicitations: “spectral function effect” (Ko) This should depend also on momentum dependence

19. Larger effects at lower energies “Threshold effect” Kaons ratio still a bit more sensitive probe: ~15% difference between DDF and NLρδ  small but perhaps measurable! 132Sn+124Sn G.Ferini et al.,PRL 97 (2006) 202301 Au+Au, 1 AGeV, central From Soft to Stiff from upper to lower curves Au+Au central: π and K yield ratios vs. beam energy energy Softer larger ratio! Opposite to mean field effect (IBUU04)! Inclusive multiplicities

20. Comparing calculations & experiments Ferini, NPA762(2005) 147 disagreement in magnitude, particularly at low energies, Threshold effect too strong Others have the opposite problem W.Reisdorf et al. NPA781 (2007) 459 Rapidity selection important central Au+Au Zhigang Xiao et al. PRL 102, 062502 (2009) Circumstantial evidences for very soft high  E sym Note when there is no Esym we are much closer among us and with data!!!

21. pp→nΔ ++ nn →pΔ - Compensation of Isospin Effects in s th due to simple assumption for  Same thresholds → the s in (NN) rules the relative yields → very important at low energies The Threshold Effect: nn → p Δ - vs pp → n Δ ++ If you have one inelastic collision how do you conserve the energy? At threshold this is really fundamental! For elatic collision the issue is not there! What is conserved is not the effective E*,p* momentum-energy but the canonical one. Increasing with momentum

22. Criticism to the present approach Problems with threshold effect calculation: 1) self-energy for  are assumed: no self consistency 2) spectral function important close to threshold reduce the effect 3) Collision integral cannot be the simple extension of the elastic one 4) mistakes… It would be important that other transport formulation join the effort Botermans, Malfliet, Phys. Rep. 198(90) “Quantum transport Theory” For elastic but with spin interaction, a step before the code approximation Conservation of Canonical momenta = 1 One recovers BUU collision integral

23. ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?

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

25. EoS of Symmetric/Neutron Matter: Hadron (NL ρ ) vs MIT-Bag → Crossings Symmetry energies hadron Quark: Fermi only symmetric neutron

26. (T,     ) binodal surface Hadron-RMF Quark- Bag model (two flavors)  trans onset of the mixed phase → decreases with asymmetry Signatures? 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 Testing deconfinement with RIB’s? Gibbs Conditions

27. Liu Bo, M.D.T., V.Greco May 09 Mixed Phase: Boundary Shifts with asymmetry  Lower Boundary much affected by the Esym  T dependence No potential E sym  Lower Boundary significantly decrease with T Upper bound

28. Quark Phase: large Isospin Distillation near the Lower Border? Signatures? Neutron migration to the quark clusters (instead of a fast emission) Large modification of isopsin particle ratio at high p T A theorethical issue : Potential Symmetry Energy in the Quark Phase? upper  quark fraction lower

29. In-Conclusion While the EOS of symmetric NM is fairly well determined, the density (and momentum) dependence of the E sym is still rather uncertain. Can it be done like for the symmetric part? Particle production Ratios      and    + are sensitive probe to high density E sym - kaon signal is a sharp signal from high density Competing effect in isospin particle ratio production: - self-energies revert the dependence respect to the n/p emission - a more careful treatment of the collision integral respect to the elastic one is essential ! E≥ 1.5 A GeV can have a transient quark phase highly asymmetricE≥ 1.5 A GeV can have a transient quark phase highly asymmetric - signatures and effective field theories to be developed - signatures and effective field theories to be developed

30. Lower  =0.0 Upper  =1.0 Symmetric to Asymmetric (not Exotic) Matter region explored ~ 1AGeV No pion excitations included

31. central Au+Au analysis of π-/π+ ratios in Au+Au Zhigang Xiao et al. PRL 102, 062502 (2009) FOPI data, W. Reisdorf et al. NPA 781 (2007) Circumstantial evidence for very soft symmetry energy

32. 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

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

34. G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005 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 Kaon ratios: comparison with experiment

35. 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.

36. Comparing with experiments Ferini, NPA762(2005) 147 disagreement in magnitude, particularly at low energies, (also in other calc.), but better at midrapidity (high density), where Kaons are produced. W.Reisdorf et al. NPA781 (2007) 459 Rapidity selection

37. In-medium Klein-Gordon eq. for K propagation: Two models for medium effects tested: 1.Chiral perturbation (Kaplan, Nelson, et al.) (ChPT) 2.One-boson-exch. (Schaffner-Bielich, et al.,) (OBE)  density and isospin dependent ChPT OBE In-Medium K energy (k=0) Splitting for K 0,+ and NL  and NL  Test of kaon potentials models Absolute yields: Ni+Ni, E=1.93 AGeV, b<4 fm, rapidity distrib. In-medium  Kaon potenial Isospin dep. part  good description od FOPI data: OBE and  eff ChPT Ratios to minimze influence of  eff kaon potentials  robust relative to K-potential, but dep.on isospin-dep part