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Many-body theory of Nuclear Matter and the Hyperon matter puzzle

Many-body theory of Nuclear Matter and the Hyperon matter puzzle. M. Baldo, INFN Catania. OUTLOOK. Many-body theory of Nuclear matter ( “old” stuff ). Can we reproduce all data extracted from phenomenology ?. The strangeness puzzle.

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Many-body theory of Nuclear Matter and the Hyperon matter puzzle

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

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

  3. Ladder diagrams for the scattering G-matrix

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

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

  6. Threehole-linecontribution

  7. Symmetric nuclear matter Evidenceofconvergence Thethreehole-linecontributionissmall inthecontinuouschoice

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

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

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

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

  12. Up tosaturation density 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

  13. Saturation point Density = 0.17 +/- 0.03 fm-3 Energy/part = -16. +/- 1. MeV Around saturation point ρ0 for symmetric matter, the binding energy is usually expanded as The parameters L and Ksym characterize the density dependence of the symmetry energy around the saturation point

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

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

  16. Getting S and L • 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

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

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

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

  20. Maximum Mass constraint PSR J1614-2230

  21. Ifneutronstars are assumedtobe composedonlyofneutrons, protons and electrons/muons, thereis at least onemicroscopic EOS thatiscompatible withphenomenologicalconstraints and itisableto produce a maximum mass ofabouttwosolarmasses. Remindthatfor a free neutron gas the maximum mass is 0.7 solar mass ! (Volkoff-Openheimer) No “exotic” componentisneeded ! 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. Free hyperons N-Y interaction included PRC 61, 055801 (2000), M.B., G. Burgio and H. Schulze Nijmegen potential for NY interaction, no YY interaction

  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. IncludingQuarkmatter 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 mattereffect The MIT bag model, CDM, NJL, FCM, DS models produce a maximum mass not largerthan 1.7 solar mass. Theycannot beconsideredcompatiblewith the “observed” NS maximum mass. Evenifweexludestrangematter .

  29. WAY OUT ? • Some additionalrepulsionispresent • for BOTH hyperons and quark matter • thatprevents the appearenceof “exotic” components in the core. • 2. The EOS forhyperon and/or quark mattermimics the EOS ofnucleonicmatter From astrophysical observations we have learned some fundamental properties of high density EOS HOWEVER ………

  30. Aaaaah ! 2.7 !!!!

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