Search for Simmetry Energy at high densityV. Greco on Behalf of the Theory Group of CataniaUniversity of CataniaINFN-LNS

Outline Symmetry energy at high density, E400 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

Symmetry EnergyHigh density/energy Probes n/p and LCP ratios p/n differential flow pions flow and ratios kaon ratios neutron stars .Liquid drop modelHow the value depends on density, .i.e. -> EOS for any n,p content Theoretical predictionsOnly Stiff- Soft is not predicted!

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

a4=Esym (r0) -> fixes (fr , fd) Similar structure in DBHF, DHF, DDC, PC-RMF, consistent with large fields observed in lQCDfd 2.0 2.5 fm2 No d fr 1.5 frFREE 15 MeV

fd = 2.5 fm2 fr 5f rFREE (50-35) MeV F. Hoffmann et al., PRC64 (2001) 034314V. Greco et al., PRC63(2001)035202Symmetry Energy in RMFT (~DBHF)Balance of isospin fields of ~ 100 MeVB.Liu, PRC65(01)045201

Important for: nucleon emission,flow, particle production (p-/p+, ... )Momentum dependenceGives a different contribution at equilibrium but in HIC Esympot(r,k)-> m*p, m*nRMFT-SkLya oppositebehavior, but there are several sources of MDMean FieldSymmetry energy

Non-relativistic massParametrize non-locality in space & timeDirac mass (for Rel.Mod.)C. Fuchs, H.H. Wolter, EPJA 30(2006)5Effective masses: different definitionsThe 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

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

Light isobar 3H/3He yieldsMass splitting: N/Z of Fast Nucleon Emission Observable very sensitive at high pTto the mass splitting and not to the asy-stiffness197Au+197Au 600 AMeV b=5 fm, y(0)0.3(squeeze-out) m*n>m*p m*n

m*n m*p197Au+197Au, 400 AMeV, b=5 fm, y(0)0.5v2 vs rapidity for 3H and 3He:Larger flow but less isospin effectsv2 vs pTV.Giordano, ECT* May 09Increasing relevance ofisospin effects for m*n

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

RBUU transport equationElastic Collision termWigner transform Dirac + Fields EquationRelativistic Vlasov Equation + Collision TermNon-relativistic BNVLorentz Force Vector Fields pure relativistic termUpper sign: nSingle particle energiesn-rich:- Neutrons see a more repulsive vector field, increasing with f and isospin density- m*n

Dynamical Effect of Relativistic Structureapproximationsr+dr0.3

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

PARTICLE PRODUCTION with different ISOSPIN: - p-/p+ vs K-/K0 - Circumstantial reasons to be careful - more theorethical efforts

Pion vs Kaon as a measure of EOSIn the 80s there was the idea of using pions to infer the EOSC.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 productionC. 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 groupshows that the situation is less drammatic that the envisaged one for p+/p- Esym~20 years after

Kaons: direct early production: high density phase isovector channel effects Au+Au@1AGeVp/K production in open system: Au+Au 1AGeV, centralProduction stopped at the maximum of the Ds production ~15 fm/c,Ks purely coming from maximum densityNot affected by p rescatterng absorption

ISOSPIN EFFECTS ON PION PRODUCTIONMain 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 pnp transformationDominant close to sub-threshold3. Isospin D-hole exicitations: spectral function effect (Ko)This should depend alsoon momentum dependence

Larger effects at lower energiesThreshold effectKaons ratio still a bit more sensitive probe:~15% difference betweenDDF and NL small but perhaps measurable!132Sn+124SnG.Ferini et al.,PRL 97 (2006) 202301Au+Au, 1 AGeV, centralFrom Soft to Stiff from upper to lower curves Au+Au central: and K yield ratios vs. beam energy energySofter larger ratio!Opposite to mean field effect(IBUU04)!Inclusive multiplicities

Comparing calculations & experimentsFerini, NPA762(2005) 147disagreement in magnitude,particularly at low energies,Threshold effect too strongOthers have the opposite problemW.Reisdorf et al. NPA781 (2007) 459Rapidity selection importantcentral Au+AuZhigang Xiao et al. PRL 102, 062502 (2009) Circumstantial evidences forvery soft high r EsymNote when there is no Esymwe are much closer among usand with data!!!

ppn++nnp-Compensation of Isospin Effects in sthdue to simple assumption for S(D)Same thresholds the sin(NN) rules the relative yields very important at low energies The Threshold Effect: nnp- vs ppn++ 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

Criticism to the present approachProblems with threshold effect calculation:1) self-energy for D are assumed: no self consistency 2) spectral function important close to threshold reduce the effect3) Collision integral cannot be the simple extension of the elastic one4) mistakesIt would be important that other transport formulation join the effortBotermans, Malfliet, Phys. Rep. 198(90) Quantum transport TheoryFor elastic but with spin interaction, a step before the code approximationConservation of Canonical momenta= 1One recoversBUU collisionintegral

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

Exotic matter over 10 fm/c? In a C.M. cellNPA775(2006)102-126

EoS of Symmetric/Neutron Matter: Hadron (NL) vs MIT-Bag CrossingsSymmetry energieshadronQuark:Fermi onlysymmetricneutron

(T,rB,rB3) binodal surfaceHadron-RMFQuark-Bag model(two flavors)rtrans onset of the mixed phase decreases with asymmetrySignatures?DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126Mixed Phase NLNLGM31 AGeV300 AMeV132Sn+124Sn, semicentralB1/4 =150 MeVTesting deconfinement with RIBs?Gibbs Conditions

Liu Bo, M.D.T., V.Greco May 09Mixed Phase: Boundary Shifts with asymmetry Lower Boundary muchaffected by the EsymdT dependenceNo potential Esym Lower Boundary significantly decrease with TUpper bound

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 pTA theorethical issue : Potential Symmetry Energy in the Quark Phase?upper

In-ConclusionWhile 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 densityCompeting 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

Lowerc=0.0Upperc=1.0Symmetric to Asymmetric (not Exotic) Matterregion explored ~ 1AGeVNo pion excitationsincluded

central Au+Auanalysis of -/+ 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

NJL Effective Lagrangian (two flavors): non perturbative ground state with q-qbar condensationM.Buballa, Phys.Rep. 407 (2005)Gap Equation 1 0 1/2 1/2Large Large T0orChiral restoration

Au+Au 1AGeV central: Phase Space Evolution in a CM cellTesting EoSCBMK production

G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005Data (Fopi)X. Lopez, et al. (FOPI), PRC 75 (2007)equilibrium (box) calculationsfinite nucleus calculations sensitivity reduced in collisions of finite nuclei single ratios more sensitive enhanced in larger systemsKaon ratios: comparison with experiment

Au+Au 1AGeV: density and isospin of the Kaon sourcen,p at High densityn/p at High densityDrop:Contribution of fast neutron emission andInelastic channels: np transformationTime interval of Kaon productioncentraldensityDynamics 2.

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

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 dependentChPTOBESplitting for K0,+and NLr and NLrdTest of kaon potentials models