The High-Density Symmetry Energy in Heavy Ion Collisions The High-Density Symmetry Energy in Heavy Ion Collisions Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept Hermann Wolter Ludwig-Maximilians-Universität München (LMU)

The High-Density Symmetry Energy in Heavy Ion Collisions The High-Density Symmetry Energy in Heavy Ion Collisions Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept Hermann Wolter Ludwig-Maximilians-Universität München (LMU) Massimo Di Toro, Maria Colonna, V. Greco, G. Ferini, (LNS Catania), Theodoros Gaitanos, (Giessen), Vaia Prassa, (Thessaloniki)

Schematic Phase Diagram of Strongly Interacting Matter Liquid-gas coexistence Quark-hadron coexistence Z/N 1 0 SIS18 neutron stars Supernovae IIa Isospin degree of freedom 1.Density dependence of the Symmetry energy in the hadronic sector 2.Investigation via heavy ion collisions 3.Observables in the above-saturation density regime: difference flows, meson ratios SIS300

Equation-of-State and Symmetry Energy BW mass formula density- asymmetry dep. of nucl.matt.     stiff soft saturation point Fairly well fixed! Soft! EOS of symmetric nuclear matter symmetry energy asymmetry  density  Symmetry energy: neutron - symm matter, rather unknown, e.g. Skyrme-like param.,B.A.Li asy-stiff asy-soft neutron matter EOS E sym pot (  ) often parametrized as Parametrizations around  0 :

C. Fuchs, H.H. Wolter, EPJA 30 (2006) 5 The Nuclear Symmetry Energy (SE) in „realistic“ models The EOS of symmetric and pure neutron matter in different many-body aproaches SE ist also momentum dependent  p/n effective mass splitting  Lane potential; mom. dep. Why is symmetry energy so uncertain?? ->In-medium  mass, and short range isovector tensor correlations (B.A. Li, PRC81 (2010));  use HIC to investigate in the laboratory and neutron star observations Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. SE nuclear matter neutron matter

E sym      MeV)     1230 Asy-stiff Asy-soft Importance of Nuclear Symmetry Energy Bayesian analysis of mass- radius relation; A. Steiner, et al., arXiv neutron stars Supernovae, very dilute matter, Cluster correlations Constraints on the Slope of SE from Structure and low-energy HIC Natowitz et al., PRL 104 (2010)

2-body collisions loss termgain term non-relativistic: BUU Vlasov eq.; mean field EOS isoscalar and isovector isospin dependent, pp,nn,pn 1)Approximation to a much more complicated non-equilibrium quantum transport equation (Kadanoff-Baym) by neglecting finite width of particles (quasi-particle approximation) 2)Relativistic equivalent available; RMF or EFT models for EOS 3)Consistency between EOS and in-medium cross sections: e.g. (Dirac) Brueckner approach 4)Isovecor effects are small relative to isoscalar quantities; differences or ratios of observables to become independent of isoscalar uncertainties 5)Collision term  dissipation, NO fluctuation term  Boltzmann-Langevin eq. Învestigation of the symmetry energy in heavy ion collisions  Transport theory

Heavy Ion Collisions at Relativistic Energies: “Flow“ Global momentum space Fourier analysis of momentum tensor : „flow“ v 2 : elliptic flowv 1 : directed flow p n asystiff asysoft asystiff Proton-neutron differential flow 132 Sn AGeV b=6fm asysoft Au+Au, 400AMeV asysoft m* n >m* p m* n <m* p Inversion of elliptic flows with effective mass Sensitivity to SE: asy-stiff more flow of neutrons, V.Giordano, M.Colonna et al., arXiv , PRC81(2010) Elliptic flow v2 But also to effective mass difference (i.e. momentum dep. of SE): Inversion of n/p potential at higher momentum

First measurement of isospin flow Each band: soft vs. stiff eos of symmetric matter, (Cozma, )  robust probe 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11)) directed flow (v1) not very sensitive, but elliptic flow (v2), originates in compressed zone determines a rather stiff symmetry energy, i.e.  =0.5  =1.5 neutron proton hydrogen ASYEOS experiment at GSI May 2011, being analyzed also study t/3He flow!

1.„direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution 2.„secondary effects“: production of particles, isospin partners  -,+, K 0,+ NN NKNK KK NN N  in-medium in-elastic   K and  potential (in- medium mass)  in-medium self-energies and width  potential, p, n Particle production as probe of symmetry energy Two limits: 1.isobar model (yield determined by CG-Coeff of  ->N  2.chemical equilibrium ->  - /  + should be good probe! box calculation Ferini et al., B.A.Li et al., PRL102  Therefore consider ratios  - /  + ; K 0 /K +

G.Ferini et al.,PRL 97 (2006) Mean field effect: U sym more repulsive for neutrons, and more for asystiff  pre-equilibrium emission of neutron, reduction of asymmetry of residue 2. Threshold effect, in medium effective masses: Canonical momenta have to be conserved. To convert to kinetic momenta, the self energies enter In inelastic collisions, like nn->p  -, the self-energies may change. Simple assumption about self energies of  Yield of particles depends on Detailed analysis gives Particle production as probe of symmetry energy (2) Two effects: Competing effects! - How taken into account in different calculations? -  dynamics may be too simple.

G.Ferini et al.,PRL 97 (2006) Central density  and K: production in high density phase Pions: low and high density phase Sensitivity to asy- stiffness Dynamics of particle production ( ,K) in heavy ion collisions  time [fm/c] Dependence of ratios on asy-stiffness: n/p ratio governs particle ratios n/p   0,- /  +,++   - /  +  K 0 /K + K 0,+ multiplicity  and  multiplicity increasing stiffness Kaons were a decisive observable to determine the symmetric EOS; perhaps also useful for SE? Kaons are closer to threshold, come only from high density, have large mean free path, small width: Ratio of K+ yield in (Au+Au)/(C+C) C. Fuchs et al., PRL 86(01)1974

MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09) MDI, x=1, very soft NL , stiff Ferini, Gaitanos,.. NPA 762 (05) NL  linear  =2, stiff Feng,… PLB 683 (10) SIII, very soft small dep. on SE J. Hong, P.Danielewicz FOPI, exp  Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459) Widely differering results of transport calculations with similar input! -  -dynamics in medium (potential, widths, etc) largely unknown - threshold and mean field effects - pion potential: U  =0 in most calculations. OK? - differences in simulations of collision term

G.Ferini et al.,PRL 97 (2006) Sn+124Sn Au+Au, 1 AGeV, central Inclusive multiplicities 132Sn+124Sn Nuclear matter (box calculation) single ratios more sensitive enhanced in larger systems - Stiffer asy-EOS  larger ratio! Opposite to mean field effect! - Kaons somewhat more sensitive than pions. esp. at low energies, close to threshold - Sensitivity reduced in finite nuclei due to evolution of asymmetry in collision Kaon production in HIC Comparision to FOPI data (Ru+Ru)/(Zr+Zr) equilibrium (box) calculations finite nucleus calculations Data (Fopi) X. Lopez, et al., PRC 75 (2007) G. Ferini, et al., NPA762(2005) 147 more asy-stiffness

 +/  - ratio B.A. Li, et al.  +/  - ratio, Feng, et al. Fermi Energy HIC, various observabl es, compilatio n MSU Present constraints on the symmetry energy Moving towards a determination of the symmetry energy in HIC but at higher density non-consistent results of simulations for pion observables. Au+Au, elliptic flow, FOPI Limits on the EOS in  -equilibrium, Including constraints from neutron stars and microscopic calc. A. Steiner, J. Lattimer, E.F.Brown, arXiv Combined methods move towards stronger constraints

Summary and Outlook EOS of symmetric NM is now fairly well determined, but density (and momentum) dependence of the Symmetry Energy rather uncertain, but important for exotic nuclei, neutron stars and supernovae. Constraints from HIC both at sub-saturation (Fermi energy regime) and supra-saturation densities (relativistic collisions), and increasingly from neutron star observables. At subsaturation densities increasingly stringent (  ~1, L~60 MeV), but constraints are largely lacking at supra-saturation densities. Observables for the supra-saturation symmetry energy N/Z of pre-equilibrium light clusters (MSU, FOPI), difference flows, (first hints -> ASYEOS) part. production rations  - /  +, K 0 /K + (FOPI,HADES) More work to do, esp. In theory (consistency of transport codes,  dynamics) Symmery energy important in the partonic phase or for the phase transition to the partonic phase? What is the SE in the partonic phase.

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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 In-Medium K energy (k=0) Test of kaon potentials models ChPT Ratios to minimze influence of  eff kaon potentials  robust relative to K-potential, but dep.on isospin- dep part ChPT OBE Splitting for K 0,+ and NL  and NL 

Strangeness ratio : Infinite Nuclear Matter vs. HIC  Au ≈0.2 (HIC)  Au ≈1.5 NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p transformation (less asymmetry in the source ) Density & asymmetry of the K-source Inf. NM G. Ferini, et al., NPA762(2005) 147 Pre-equilibrium emission (mainly of neutrons) reduced asymmetry of source for kaon production  reduces sensitivity relative to equilibrium (box) calculation

asy-stiff asy-soft Light isobar 3 H/ 3 He yields 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 m* n >m* p m* n <m* p V.Giordano, M.Colonna et al., PRC 81(2010) asy-stiff asy-soft Crossing of the symmetry potentials for a matter at ρ≈1.7ρ 0 n/p ratio yields Pre-equilibrium nucleon and light cluster emission at higher energy

Differential elliptic flow asystiffasysoft m* n >m* p m* n <m* p Inversion of elliptic flows because of inversion of potentials with effective mass W. Reisdorf, ECT*, May 09 Indication of experimental effect Au+Au, 400 AMeV t- 3 He pair similar but weaker Au+Au, 600 AMeV Elliptic flow more sensitive, since determined by particles that are emitted perp to the beam direction V.Giordano, M.Colonna et al., arXiv , PRC81(2010)

Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459) Many attempts to understand behaviour: Double ratio of Sn+Sn systems Yong, et al.,PRC73,034603(06) Sensitivity=Y(x=1)/Y(x=0) Zhang, et al., PRC80,034616(09) Possible causes: - Pion are created via  ‘s.  dynamics in medium (potential, width, etc) largely unknown. - Threshold and mean field effects - Pion potential: U  =0 in most calculations. OK? - differences in simulations, esp. collision term - Urgent problem to solve!!!

Transverse Pion Flows FOPI: W.Reisdorf et al. NPA781 (2007) 459 Antiflow: decoupling of the pion/nucleon flows OK general trend. but: - smaller flow for both  - and  + -not much dependent on Iso-EoS IQMD softMD FOPI IQMD stiffMD Au+Au General behaviour (centrality dep.) ++ -- -- ++ -- -- ++ ++ Simulations: V.Prassa, PhD Sept.07 Rapidity dependence

stiff soft asy-stiff asy-soft C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. The Nuclear Symmetry Energy in different „realistic“ models The EOS of symmetric and pure neutron matter in different many- body aproaches SE asy-soft at  0 (asystiff very similar) Isovector (Lane) potential: momentum dependence SE ist also momentum dependent  p/n effective mass splitting Why is symmetry energy so uncertain?? ->In-medium  mass, and short range tensor correlations (B.A. Li, PRC81 (2010));

Neutron stars: a laboratory for the high-density symmetry energy A normal NS (n,p,e) … or exotic NS ?? Typical neutron stars Neutron star mass dep. on Symmetry Energy proton fraction x Onset of direct URCA (x>1/9) Fast cooling of NS: direct URCA process Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006)

Neutron star cooling: a test of the symmetry energy A given symmetry energy behavior leads to a distribution of NS masses: Comparison to mass distribution from population synthesis models (Popov et al., A&A 448 (2006) plus other neutron star observables; consistency far from obvious e.g. for DBHF EOS ) D. Blaschke, Compstar workshop, Caen, 10

Limits on the EoS from a Bayesian analysis of NS mass-Radius observations A. Steiner, J. Lattimer, E.F.Brown, arXiv Comparison to models many Skyrme models eliminated Limits on the EOS in  -equilibrium Limits on SE power  law  Lattimer, Lim, arxiv Synthesis of constraints..but measurement in very different density ranges!

Astrophysics: Supernovae and neutron stars A normal NS (n,p,e) or exotic NS? PSR J typical neutron stars heaviest neutron star Onset of direct URCA: Y p >.11; Too fast cooling central density Comparison to models many Skyrme models eliminated Limits on the EoS from a Bayesian analysis of NS mass-Radius observations A. Steiner, J. Lattimer, E.F.Brown, arXiv

Deconfinement Transition with Large Asymmetry EOS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings DiToro,et al.,, NPA775(2006) Quark: Fermi only symmetric neutron NLρ NLρδ GM3 1 AGeV 300 AMeV 132Sn+124Sn, semicentral B 1/4 =150 MeV Hadron Symmetry energy