From the Phys.Dept. Jan.2002Etna Double-Face, Aug.07ISOSPIN EFFECTS on PHASE TRANSITIONSof HADRONIC to QUARK MATTER M.Colonna, V.Baran, M.Di Toro, V. Greco, Liu Bo, S. PlumariLNS-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, 2008From the EtnaMelting Pot

Tentative Plan of the Talk1. Homework Symmetry Energy The problem at High Baryon Density2. Quantum-Hadro-Dynamics: EoS Fully Covariant Transport, Essential Mean Field Effects Elliptic Isospin Flows, Meson Production3. Transition to a Mixed Phase at High Baryon and Isospin density

HOMEWORKHadron-Quark EoS at High Baryon DensityHadron : STANDARD EoS (with Symmetry Term)Quark: STANDARD MIT-Bag ModelISOSPIN EFFECTS on the MIXED PHASEZero Temperature: two pages with a pencil.

EoS of Symmetric/Neutron Matter: Hadron (NL) vs MIT-Bag CrossingsSymmetry energieshadronQuark:Fermi onlysymmetricneutronGluon s0 Softer quark EoST=0, Gluon s=0

o o o ox x x xNNZZkF Symmetric AsymmetricFermi(T=0) F/3 ~ 2/3Interaction (nucleon sector)Two-body ~ , many-body correlations?Symmetry Energya4 term (~30MeV) of the Weiszcker Mass Formula: at saturation Esym(Fermi) Esym(Interaction)E/A () = E() + Esym()II=(N-Z)/A search for ~ but can be density dependent momentum dependence? neutron/proton mass splitting

EOS of Symmetric and Neutron MatterDirac-BruecknerVariational+3-body(non-rel.)RMF(NL3)Density-Dependent couplingsChiral PerturbativeCh.Fuchs, H.H.Wolter, WCI Final Report EPJA 30 (2006) 5-21symmetricAFDMCV8+3bodyFantoni et al0807.5043Consensus on aStiff Symmetry Termat high density?

NN scattering nuclear interaction from meson exchange: main channels (plus correlations) s(0+,0) w(1-,0) d(0+,1) r(1-,1)IsoscalarIsovectorOBEScalarVectorScalarVectorNuclear interaction by Effective Field Theoryas a covariant Density Functional ApproachQuantum Hadrodynamics (QHD) Relativistic Transport Equation (RMF)Relativistic structure alsoin isospin space ! Esym= kin. + (r-vector) ( d-scalar)

a4=Esym (r0) fixes (fr , fd) DBHF DHFfd 2.0 2.5 fm2 No d fr 1.5 frFREE

fd = 2.5 fm2 fr 5f rFREE Liu Bo et al., PRC65(2002)045201RMF Symmetry Energy: the - mechanism NL NL NLConstant Coupling Expectations

Self-Energies: kinetic momenta and (Dirac) effective massesUpper sign: nDirac dispersion relation: single particle energiesQHD Relativistic Mean Field Transport Equationn-rich:- Neutrons see a more repulsive vector field, increasing with f and isospin density- m*(n)

RMF (RBUU) transport equationCollision term:Wigner transform Dirac + Fields EquationRelativistic Vlasov Equation + Collision TermNon-relativistic Boltzmann-Nordheim-Vlasovdriftmean fieldLorentz Force Vector Fields pure relativistic term

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

Evidences of a STIFF Symmetry term at high baryon densityCollective Flows:v2 Flow: Large Squeeze-Out for n-rich clusters (e.g. t vs 3He at high pT)Meson Production -/+ increase above the threshold K 0/K+ yield ratio (no pT selection)FOPI data (W.Reisdorf, ECT* May 2009) at SIS energies,

More to come from the LAND-CHIMERA-ALADIN Proposal at GSI

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)

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

Testing deconfinement with RIBs?(T,rB,r3) binodal surfaceHadron-RMFQuark-Bag model(two flavors)rtrans onset of the mixed phase decreases with asymmetryDiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126Mixed Phase NLNLGM31 AGeV300 AMeV132Sn+124Sn, semicentralB1/4 =150 MeV

Mixed Phase: Boundary Shifts at Low Temperature Lower Boundary muchaffected by the Symmetry EnergyNLNLNLIsospin asymmetry

mu=md=5.5MeV=0.0=1.0Critical End-Point for Symmetric Matter?NL, NL,NL

Lower=0.0Upper=1.0Symmetric to Asymmetric (not Exotic) MatterNL

upperupperlowerNL :more repulsive high densitySymmetry Energyin the hadron phaseInside the Mixed Phase (asymmetry =0.2)Long way to reach 20% quark matter, butlower=0.5=0.2=0.2=0.5NLNLDependence on theHigh Density Hadron EoS

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

=0.2=0.2=0.5=0.5=0.2=0.2=0.5=0.52. Baryon Densities in the Two PhasesNLNLLarger Baryon Density in the Quark Phase Signatures?

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

M.Buballa, Phys.Rep. 407 (2005)Parameters: p, G, m vs.M, f, (estimation)B=0T=0mu,d=5.5MeVmu,d=0.0NJL Phase Diagram q

S.Plumari, Thesis 2009Standard Parameters Coexistence Spinodal

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

Neutron-rich matter at high baryon density:|d| decreases more rapidly due to the larger d

(u d) < 0 in the range 0.15 to 0.25

Very n-rich matter: I=(N-Z)/A=0.4

Masses in the Chiral Phase =0.2 =1Solutions of the Iso-Gap Equation S.Plumari, Thesis 2009Iso-NJLm = 6MeV = 590MeVG02=2.435Mvac=400MeV=(-241.5MeV)3m=140.2MeVf=92.6MeV

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

Conclusions for the Physics at NICAIsospin dependence of the Mixed Phase Signatures( reduced v2 at high pT, nq-scaling break down. )Isospin Trapping: Reduction of n-rich cluster emission Anomalous production of Isospin-rich hadrons at high pT u-d mass splitting (mu >md)ExperimentsTheoryIsospin effects on the spinodal decompositionIsovector Interaction in Effective QCD LagrangiansLarger Baryon Density in the Quark Phase: - Large Yield of Isospin-rich Baryons at high pT

Nuclear Matter Phase Diagram.NICA updatedEvery Complex Problem has a Simple Solutionour journey is around here.most of the time Wrong (Umberto Eco)Conclusion:

Back-up Slides

Bag-Model EoS: Relativistic Fermi Gas (two flavors)Energy densityPressureNumber densityq, qbarFermi DistributionsBaryon/Isospin Densitiesand Chemical Potentialsonly kinetic symmetry energy

NN-STARS: Present status with observation constraintsD.Page, S.Reddy, astro-ph/0608360, Ann.Rev.Nucl.Part.Sci. 56 (2006) 327Softer EOSsmaller R (larger -central), smaller maximum MassThe broad range of predicted radii for nucleon EOS will be narrowed inthe near future owing toneutron-skin thickness andprobably also to heavy-ion experimentsGeneralRelativityAAAAAA

Proton fraction, y=Z/A, fixed by Esym() at high baryon density:-equilibriumCharge neutrality, e=p=yFast cooling: Direct URCA processFermi momenta matching

Neutron Star (npe) propertiesDirect URCA thresholdMass/Radius relationNLNLNLNLDD-FDD-Fcompact stars & heavy ion dataT.Klaehn et al. PRC 74 (2006) 035802- Transition to quark matter?- Faster Cooling for Heavier NS?

DIRAC OPTICAL POTENTIALDispersion relationSchrdinger massupper signs: neutronAsymmetric MatterRMFPhys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82~50 MeVDirac mass

BEYOND RMF: k-dependence of the Self-EnergiesSchroedinger massAsymmetric MatterDBHFHigh momentum saturation of the optical potentialHigh momentum increase of the Dirac MassPhys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82Problem still open..sensitive observables

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

Isospin Flows at Relativistic EnergiesEsym(): Sensitivity to the Covariant StructureEnhancement of the Isovector-vector contribution via the Lorentz Force High p_t selections: source at higher density Symmetry Energy at 3-40

Au+Au 800 A MeV elliptic flows, semicentralRapidity selectionsv2(n) |y| < 0.5v2(n), v2(p) vs. p_tv2(p)All rapiditiesv2(n)v2(p)Low p_t spectator contributions

Elliptic flow Differenceapproximationsr+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?High pt selection CHIMERA-LAND-ALADIN Proposal at SIS-GSI andR3B(FAIR)

Meson Production at Relativistic Energies: -/ +, K 0/K + Esym(): Sensitivity to the Covariant Structure Self-energy rearrangement in the inelastic vertices withdifferent isospin structure large effects around the thresholdsHigh p_t selections: source at higher density Symmetry Energy at 3-40

PION PRODUCTIONMain mechanism 2. Fast neutron emission: mean field effect1. C.M. energy available: threshold effectVector self energy more repulsive for neutrons and more attractive for protonsSome compensationin open systems, HIC,but threshold effect more effective, in particular at lowenergiesnp transformationnnn0n-p-p+n++n+p+ppp-(-) enhanced(+) reducedG.Ferini et al., NPA 762 (2005) 147, NM Box PRL 97 (2006) 202301, HICNo evidence of Chemical Equilibrium!!

The Threshold Effect: nnp- vs ppn++ The Threshold Effect: nnp- vs ppn++ ppn++nnp-Compensation of Isospin EffectsAlmost same thresholds the sin(NN) rules the relative yields very important at low energies increasenear threshold

Pion/Kaon production in open system: Au+Au 1AGeV, centralPions: large freeze-out, compensation Kaons: early production: high density phase isovector channel effects but mostly coming from second step collisions reduced asymmetry of the sourceG.Ferini et al.,PRL 97 (2006) 202301Increasing EsymIncreasing Esym

Kaon production in open system: Au+Au 1AGeV, central Main ChannelsK0 vs K+:opposite contribution of the -coupling.but second steps

NN BYK--------- N BY BYK N YK YK

Au+Au central: Pi and K yield ratios vs. beam energyPions: less sensitivity ~10%, but larger yieldsK-potentials:similar effectson K0, K+Kaons:~15% difference betweenDDF and NLInclusive multiplicities132Sn+124SnG.Ferini et al.,PRL 97 (2006) 202301

Equilibrium Pion Production : Nuclear Matter Box Results Chemical EquilibriumDensity and temperature like in Au+Au 1AGeV at max.compression (~20, T~50MeV) vs.asymmetryLarger isospin effects: - no neutron escape - s in chemical equilibrium, less n-p transformation NPA762(2005) 147~ 5 (NL) to 10 (NL)Dynamics 1.

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.

Kaon ratios: comparison with experimentG. Ferini, et al., NPA 762 (2005) and PRL 97 (2006)Data (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 systems larger asymmetries more exclusive data H.Wolter, ECT* May 09

Nuclear Matter Box ResultsDensity and temperature like in Au+Au 1AGeV at max.compression vs.asymmetryLarger isospin effects: - no neutron escape - s in chemical equilibriumless n-p transformation NPA762(2005) 147

Density r/r0 Temperature 20 200 MeV Plasma of Quarks and Gluons 1: nuclei 5?Phases of Nuclear MatterPhilippe Chomaz artistic viewIsospin ?Mixed PhaseIn terrestrialLabs.?

Lower Boundary of the Binodal Surface vs. NM Asymmetryvs. Bag-constant choiceProton-fractionsymmetricNPA775(2006)102-126 = 1-2 Z/A