1. Many-body theory of Nuclear Matter and the Hyperon matter puzzle M. Baldo, INFN Catania

2. Many-body theory of Nuclear matter ( “old” stuff ) Can we reproduce all data extracted from phenomenology ? OUTLOOK The strangeness puzzle Constraints on the “exotic” components

3. Ladder diagrams for the scattering G-matrix

4. Two and three hole-line diagrams in terms of the Brueckner G-matrixs The BBG expansion

5. The ladder series for the three-particle scattering matrix

6. Three hole-line contribution

7. Evidence of convergence The three hole-line contribution is small in the continuous choice Symmetric nuclear matter

8. Neutron matter Using different prescription s for the auxiliary potential. Neutron matter

9. Microscopic EOS of symmetric and neutron matter Introducing three-body forces EOS from BBG EOS of Akmal & Pandharipande

10. M.B. & C. Maieron, PRC 77, 015801 (2008) A.Gezerlis and J. Carlson, Pnys. Rev. C 77,032801 (2008) Quantum Monte Carlo calculation Neutron matter at very low density

11. M.B. & C. Maieron, PRC 77, 015801 (2008) QMC

12. Developing a density functional from nuclear matter to finite nuclei following Khon-Sham scheme. M.B., P.Schuck and X. Vinas, PLB 663, 390 (2008) arXiv:1210.1321 Average deviation for the total binding energy d(E) = 1.58 MeV Competitive with the best density functional s Up to saturation density

13. The parameters L and K sym characterize the density dependence of the symmetry energy around the saturation point 13 Around saturation point ρ 0 for symmetric matter, the binding energy is usually expanded as Saturation point Density = 0.17 +/- 0.03 fm-3 Energy/part = -16. +/- 1. MeV

14. Symmetry energy Boundaries by P. Danielewicz 2012, from IAS analysis

15. 213 230 +/- 30 31.9 30 +/- 35 -96.75 -200 --- 150 52.96 55 +/- 25 Theory Phen. Nuclear matter physical parameters near saturation FURTHER CONSTRAINTS AROUND SATURATION M. Dutra et al., PRC85, 035201 (2012) M.B. Tsang et al., PRC86, 015803 (2012)

16. Kortelainen et al., PRC 2010 Chen et al., PRC 2010 Piekarewicz et al., 1201.3807 Trippa et al., PRC2008 Tsang et al., PRL2009 Steiner et al., ApJ2010 Lattimer & Lim, arXiv:1203.4286 Getting S and L

17. HIGHER DENSITY CONSTRAINTS FROM HEAVY ION REACTIONS K+ Flow K+ : Lynch et al., Prog. Part. Nucl. Phys. 62, 427 (2009) Flow : Danielewicz et al., Science 298, 1592 (2002) EOS

18. Andrew A. Steiner et al., ApJ 722, 33 (2010) Inference from 6 NS data on X-ray bursts or transients Boundaries to the eos from astrophysical observations Together with heavy-ion contraints it is tested the symmetry energy at high density

19. DU process test …………….. QPO Cooling Other EOS tests, T. Klahn et al., PRC, 035802 (2006) Superluminal speed of sound

20. PSR J1614-2230 Maximum Mass constraint

21. If neutron stars are assumed to be composed only of neutrons, protons and electrons/muons, there is at least one microscopic EOS that is compatible with phenomenological constraints and it is able to produce a maximum mass of about two solar masses. Remind that for a free neutron gas the maximum mass is 0.7 solar mass ! (Volkoff-Openheimer) No “exotic” component is needed ! BUT …….

22. Looking at the chemical potentials of neutrons, protons and hyperons Nijmegen soft core potential for hyperon-nucleon interaction PRC 58, 3688 (1998)

23. PRC 61, 055801 (2000), M.B., G. Burgio and H. Schulze Nijmegen potential for NY interaction, no YY interaction Free hyperons N-Y interaction included

24. Softening of the EOS The N-Y interaction produces a slightly repulsive effect on the EOS The huge softening is mainly due to the presence of additonal degrees of freedom

25. Drastic decrease of the maximum mass if Hyperons interact according to standard potential s tuned at saturation

26. Other 3BF and BHF variants Compensation effects between stiffness and Hyperon fraction

27. Including Quark matter Since we have no theory which describes both confined and deconfined phases, one has to use two separate EOS for baryon and quark matter and look at the crossing in the P-chemical potential plane Try Quark matter EOS. MIT bag model Nambu-Jona Lasinio Coloror dielectric model FCM model Dyson-Schwinger model

28. Summarizing the quark matter effect The MIT bag model, CDM, NJL, FCM, DS models produce a maximum mass not larger than 1.7 solar mass. They cannot be considered compatible with the “observed” NS maximum mass. Even if we exlude strange matter.

29. WAY OUT ? 1.Some additional repulsion is present for BOTH hyperons and quark matter that prevents the appearence of “exotic” components in the core. 2. The EOS for hyperon and/or quark matter mimics the EOS of nucleonic matter From astrophysical observations we have learned some fundamental properties of high density EOS HOWEVER ………

30. Aaaaah ! 30 2.7 !!!!