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Search for Simmetry Energy at high density

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

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Search for Simmetry Energy at high density

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  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 Esym • n/p, 3H/3He ratio & flows (impact of m*n,p) • particle production (p+/p-, K0/K+) • Dependence of QGP transition on isospin • Strong isospin fractionation (large asymmetry in the quark phase) - implementation in the transport codes -> signatures

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

  4. Isospin degrees of freedom in QHD QHD-I meson-like fields exchange model • s - w model Only kinetic contribution to Esym QHD-II • Charged mesons : (scalar isovector) (vector-isovector) Relativistic structure also in isospin space ! Esym= cin. + (r-vector) – (d-scalar) The Dirac equation becomes: Splitting n & p M*

  5. r r+d r * d Symmetry Energy in RMFT (~DBHF) B.Liu, PRC65(01)045201 No dfr1.5 frFREE 15 MeV fd =2.5 fm2 fr 5frFREE(50-35) MeV fd 2.0 2.5 fm2 a4=Esym (r0) -> fixes (fr , fd) F. Hoffmann et al., PRC64 (2001) 034314 V. Greco et al., PRC63(2001)035202 Similar structure in DBHF, DHF, DDC, PC-RMF, … consistent with large fields observed in lQCD Balance of isospin fields of ~ 100 MeV

  6. m*n < m*p Lane potential m*n > m*p data Momentum dependence Mean Field Symmetry energy Gives a different contribution at equilibrium but in HIC Esympot(r,k) -> m*p, ≠ m*n RMFT-SkLya opposite behavior, but there are several sources of MD… Important for: nucleon emission, flow, particle production (p-/p+, ... )

  7. Diffence in proton/neutron effective masses Dirac-RMFT Effective masses:different definitions Non-relativistic mass Parametrize non-locality in space & time Dirac mass (for Rel.Mod.) C. Fuchs, H.H. Wolter, EPJA 30(2006)5 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

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

  9. asy-stiff asy-soft Mass splitting: N/Z of Fast Nucleon Emission Light isobar 3H/3He yields n/p ratio yields 197Au+197Au 600 AMeV b=5 fm, y(0)0.3 (squeeze-out) asy-stiff • m*n>m*p • m*n<m*p asy-soft Observable very sensitive at high pT to the mass splitting and not to the asy-stiffness Crossing of the symmetry potentials for a matter at ρ≈1.7ρ0 V.Giordano, ECT* May 09

  10. m*n>m*p m*n<m*p Mass splitting impact on Elliptic Flow V.Giordano, ECT* May 09 197Au+197Au, 400 AMeV, b=5 fm, y(0)0.5 m*n<m*p : larger neutron squeeze out at mid-rapidity - Larger neutron repulsion for asy-stiff Increasing relevance of isospin effects for m*n<m*p v2 vs pT v2 vs rapidity for 3H and 3He: Larger flow but less isospin effects m*n > m*p v2 vs Y/Y0 m*n < m*p

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

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

  13. Dynamical Effect of Relativistic Structure 132Sn+132Sn, 1.5AGeV, b=6fm fr, fd determined from p-n v2 flow r+d Equilibrium (ρ,δ) dynamically broken: Importance of the covariant structure r approximations 0.3<Y/Yproj<0.8 r+d r Dynamical boosting of the Isopin effect that is larger when fr is larger V. Greco et al. PLB562 (2003) V.Greco et al., PLB562(2003)215

  14. W.Reisdorf, ECT* May 09: FOPI 3H-3He V2 Results Au+Au with increasing beam energy Hunting isospin with v2 : the mass 3 pair A small gradual change in The difference 3H-3He when Raising the beam energy for Au+Au (N/Z = 1.5) Relativistic Lorentz effect? The vector part of the isovector gets dynamically enhanced at E~1.5 AGeV(V. Greco et al. PLB562 (2003))

  15. PARTICLE PRODUCTION with different ISOSPIN: - p-/p+ vs K-/K0 - 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 p+/p- <-> Esym ~20 years after

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

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

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

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

  21. The Threshold Effect: nn→pΔ- vs pp→nΔ++ nn→pΔ- Increasing with momentum pp→nΔ++ Compensation of Isospin Effects in sth due to simple assumption for S(D) Same thresholds → the sin(NN)rules the relative yields → very important at low energies 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.

  22. Criticism to the present approach Problems with threshold effect calculation: 1) self-energy for D 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… For elastic but with spin interaction, a step before the code approximation = 1 One recovers BUU collision integral Conservation of Canonical momenta Botermans, Malfliet, Phys. Rep. 198(90) “Quantum transport Theory” It would be important that other transport formulation join the effort

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

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

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

  26. Testing deconfinement with RIB’s? Gibbs Conditions Mixed Phase → Hadron-RMF B1/4 =150 MeV NLρ (T,rB,rB3) binodal surface Quark- Bag model (two flavors) NLρδ GM3 1 AGeV rtrans onset of the mixed phase → decreases with asymmetry 300 AMeV 132Sn+124Sn, semicentral Signatures? DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126

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

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

  29. In-Conclusion • While the EOS of symmetric NM is fairly well determined, the density (and momentum) dependence of the Esym is still rather uncertain. • Can it be done like for the symmetric part? Particle production • Ratios p-/p+and K0/K+ are sensitive probe to high density Esym • - 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 asymmetric • - signatures and effective field theories to be developed

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

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

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

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

  34. Comparision to FOPI data (Ru+Ru)/(Zr+Zr) Kaon ratios: comparison with experiment G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005 equilibrium (box) calculations finite nucleus calculations • sensitivity reduced in collisions of finite nuclei • single ratios more sensitive • enhanced in larger systems Data (Fopi) X. Lopez, et al. (FOPI), PRC 75 (2007)

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

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

  37. ChPT Absolute yields: Ni+Ni, E=1.93 AGeV, b<4 fm, rapidity distrib. Ratios to minimze influence of seff kaon potentials In-medium s Isospin dep. part Kaon potenial In-Medium K energy (k=0)  robust relative to K-potential, but dep.on isospin-dep part  good description od FOPI data: OBE and seff Test of kaon potentials models 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 Splitting for K0,+ and NLr and NLrd OBE

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