The High-Density Symmetry Energy in Heavy Ion Collisions

1. The High-Density Symmetry Energy in Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München (LMU) Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012

2. The High-Density Symmetry Energy in Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München (LMU) Massimo Di Toro, Maria Colonna, V. Greco, G. Ferini, (LNS Catania), Theodoros Gaitanos, (Giessen), Vaia Prassa, (Thessaloniki) Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012

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

4. neutron matter EOS Symmetry energy: neutron - symm matter, rather unknown, e.g. Skyrme-like param.,B.A.Li EOS of symmetric nuclear matter asy-stiff stiff asy-soft soft Parametrizations around r0 : rB/r0 Esympot(r) often parametrized as saturation point Fairly well fixed! Soft! Equation-of-State and Symmetry Energy symmetry energy BW mass formula density-asymmetry dep. of nucl.matt. density r asymmetry d

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

6. Supernovae, very dilute matter, Cluster correlations neutron stars Asy-stiff Esym(rB)(MeV) Constraints on the Slope of SE from Structure and low-energy HIC Asy-soft 0 1 rB/r0 2 3 Bayesian analysis of mass-radius relation; A. Steiner, et al., arXiv 1205.6871 Importance of Nuclear Symmetry Energy Natowitz et al., PRL 104 (2010)

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

8. Global momentum space Au+Au, 400AMeV asysoft m*n>m*p But also to effective mass difference (i.e. momentum dep. of SE): Inversion of n/p potential at higher momentum Elliptic flow v2 v1: directed flow v2: elliptic flow m*n<m*p asystiff Inversion of elliptic flows with effective mass V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010) Heavy Ion Collisions at Relativistic Energies: “Flow“ Fourier analysis of momentum tensor : „flow“ 132Sn + 132Sn @ 1.5 AGeV b=6fm asystiff asysoft Sensitivity to SE: asy-stiff more flow of neutrons, n p <px(y)> Proton-neutron differential flow asysoft <pxp-n(y)>

9. Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11)) neutron proton hydrogen directed flow (v1) not very sensitive, but elliptic flow (v2), originates in compressed zone determines a rather stiff symmetry energy, i.e. g=0.5 g=1.5 Each band: soft vs. stiff eos of symmetric matter, (Cozma, 1102.2728)  robust probe First measurement of isospin flow ASYEOS experiment at GSI May 2011, being analyzed also study t/3He flow!

10. Particle production as probe of symmetry energy B.A.Li et al., PRL102 NN ND p, n LK NLK Np in-medium in-elastic s , K and L potential (in-medium mass) D in-medium self-energies and width p potential , • Two limits: • isobar model • (yield determined by CG-Coeff of D->Np • 2. chemical equilibrium • -> p-/p+should be good probe! box calculation Ferini et al., • „direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution • „secondary effects“: production of particles, isospin partners p-,+, K0,+ Therefore consider ratios p-/p+; K0/K+

11. Particle production as probe of symmetry energy (2) Two effects: 1. Mean field effect: Usym 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->pD-, the self-energies may change. Simple assumption about self energies of D.. Yield of particles depends on Detailed analysis gives Competing effects! - How taken into account in different calculations? - D dynamics may be too simple. G.Ferini et al.,PRL 97 (2006) 202301

12. Ratio of K+ yield in (Au+Au)/(C+C) 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: C. Fuchs et al., PRL 86(01)1974 Dynamics of particle production (D,p,K) in heavy ion collisions Au+Au@1AGeV G.Ferini et al.,PRL 97 (2006) 202301 Central density D and K: production in high density phase Pions: low and high density phase Sensitivity to asy-stiffness Dependence of ratioson asy-stiffness: n/p ratio governs particle ratios n/p D0,-/D+,++  p-/p+ K0/K+ p and D multiplicity K0,+ multiplicity increasing stiffness  time [fm/c]

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

14. Comparision to FOPI data Au+Au, 1 AGeV, central (Ru+Ru)/(Zr+Zr) equilibrium (box) calculations 132Sn+124Sn Data (Fopi) X. Lopez, et al., PRC 75 (2007) finite nucleus calculations Nuclear matter (box calculation) 132Sn+124Sn Inclusive multiplicities G. Ferini, et al., NPA762(2005) 147 G.Ferini et al.,PRL 97 (2006) 202301 Kaon production in HIC more asy-stiffness • - 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 • single ratios more sensitive • enhanced in larger systems

15. Limits on the EOS in b-equilibrium, Including constraints from neutron stars and microscopic calc. Au+Au, elliptic flow, FOPI A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871 Combined methods move towards stronger constraints Present constraints on the symmetry energy p+/p- ratio, Feng, et al. Fermi Energy HIC, various observables, compilation MSU p+/p- ratio B.A. Li, et al. Moving towards a determination of the symmetry energy in HIC but at higher density non-consistent results of simulations for pion observables.

16. 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 (g~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 p-/p+ , K0/K+ (FOPI,HADES) • More work to do, esp. In theory (consistency of transport codes, p,D 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.

17. Thank you

18. Backup

19. ChPT Splitting for K0,+ and NLr and NLrd ChPT OBE Ratios to minimze influence of seff kaon potentials In-Medium K energy (k=0)  robust relative to K-potential, but dep.on isospin-dep part Test of kaon potentials models 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

20. Density & asymmetry of the K-source aAu≈0.2 Au+Au@1AGeV (HIC) N/ZAu≈1.5 Inf. NM NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p transformation (less asymmetry in the source) Strangeness ratio : Infinite Nuclear Matter vs. HIC 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

21. Pre-equilibrium nucleon and light cluster emission at higher energy asy-stiff asy-soft 197Au+197Au 600 AMeV b=5 fm, y(0)0.3 Light isobar 3H/3He yields n/p ratio yields asy-stiff • m*n>m*p • m*n<m*p asy-soft Crossing of the symmetry potentials for a matter at ρ≈1.7ρ0 Observable very sensitive at high pT to the mass splitting and not to the asy-stiffness V.Giordano, M.Colonna et al., PRC 81(2010)

22. Au+Au, 600 AMeV Inversion of elliptic flows because of inversion of potentials with effective mass t-3He pair similar but weaker W. Reisdorf, ECT*, May 09 Indication of experimental effect Differential elliptic flow Au+Au, 400 AMeV asystiff asysoft m*n>m*p m*n<m*p V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010) Elliptic flow more sensitive, since determined by particles that are emitted perp to the beam direction

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

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

25. asy-soft at r0 (asystiff very similar) SE ist also momentum dependent  p/n effective mass splitting stiff Isovector (Lane) potential: momentum dependence soft asy-stiff asy-soft The Nuclear Symmetry Energy in different „realistic“ models Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. The EOS of symmetric and pure neutron matter in different many-body aproaches C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) SE Why is symmetry energy so uncertain?? ->In-medium r mass, and short range tensor correlations (B.A. Li, PRC81 (2010));

26. Neutron star mass dep. on Symmetry Energy Fast cooling of NS: direct URCA process proton fraction x Typical neutron stars Onset of direct URCA (x>1/9) Neutron stars: a laboratory for the high-density symmetry energy A normal NS (n,p,e) … or exotic NS ?? Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

27. 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 Neutron star cooling: a test of the symmetry energy e.g. for DBHF EOS) D. Blaschke, Compstar workshop, Caen, 10

28. Comparison to models many Skyrme models eliminated Limits on SE powerlaw g Limits on the EOS in b-equilibrium Synthesis of constraints Lattimer, Lim, arxiv 1203.4286 Limits on the EoS from a Bayesian analysis of NS mass-Radius observations A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871 ..but measurement in very different density ranges!

29. Comparison to models many Skyrme models eliminated PSR J1614-2730 typical neutron stars heaviest neutron star Onset of direct URCA: Yp>.11; Too fast cooling Limits on the EoS from a Bayesian analysis of NS mass-Radius observations A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871 central density Astrophysics: Supernovae and neutron stars A normal NS (n,p,e) or exotic NS?

30. Deconfinement Transition with Large Asymmetry B1/4 =150 MeV NLρ NLρδ GM3 1 AGeV Hadron Symmetry energy 300 AMeV 132Sn+124Sn, semicentral EOS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings Quark: Fermi only symmetric neutron DiToro,et al.,, NPA775(2006)102-126