Many-body theory of Nuclear Matterand the Hyperon matter puzzle

M. Baldo, INFN Catania

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

Ladder diagrams for the scattering G-matrix

Ge

QVVG

Two and three hole-line diagrams in terms of the Brueckner G-matrixs

The BBG expansion

The ladder series for the three-particlescattering matrix

A

Akkk kk

h

kkGkke

kkkXXTkkke

kkGkk

E

Te

QGXGT

212''1

3213321

2]'''[

121

3

33

3

||'''

1''''||''

1

''||2

1

321

F

F

kkkkk

kkkk

'','',','

,,

2121

321

Three hole-line contribution

Evidence of convergenceThe three hole-line contribution is small

in the continuous choice

Symmetric nuclear matter

Neutron matter

Using different prescription s for the auxiliary potential.

Neutron matter

Microscopic EOS of symmetric and neutron matterIntroducing three-body forces

EOS from BBG

EOS of Akmal & Pandharipande

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

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

QMC

Developing a density functionalfrom nuclear matter to finitenuclei following Khon-Sham

scheme.M.B., P.Schuck and X. Vinas,

PLB 663, 390 (2008)

arXiv:1210.1321

Average deviation for thetotal binding energy

d(E) = 1.58 MeV

Competitive with the bestdensity functional s

Up to saturation density

The parameters L and Ksym characterize the density dependence of the symmetry energy around the saturation point

1313

Around saturation point ρ0 for symmetric matter, the binding energy is usually expanded as

Saturation pointDensity = 0.17 +/- 0.03 fm-3 Energy/part = -16. +/- 1. MeV

Symmetry energy

Boundaries by P. Danielewicz 2012, from IAS analysis

213 230 +/- 30

31.9 30 +/- 35

-96.75 -200 --- 150

52.96 55 +/- 25

Theory Phen.

Nuclear matter physical parameters near saturation

FURTHER CONSTRAINTSAROUND SATURATION

M. Dutra et al. , PRC85, 035201 (2012)M.B. Tsang et al., PRC86, 015803 (2012)

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

HIGHER DENSITYCONSTRAINTS 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

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

DU process test

……………..

QPO

Cooling

Other EOS tests, T. Klahn et al., PRC, 035802 (2006)

Superluminal speed of sound

PSR J1614-2230

Maximum Mass constraint

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 andit 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 …….

Looking at the chemical potentials of neutrons , protons and hyperons

np

ep

n

pn

e

epn

2

Nijmegen soft core potentialfor hyperon-nucleon interaction

PRC 58, 3688 (1998)

PRC 61, 055801 (2000), M.B., G. Burgio and H. Schulze

Nijmegen potential for NY interaction, no YY interaction

Free hyperons

N-Y interactionincluded

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

Drastic decrease of the maximum mass if Hyperons interact according to standard

potential s tuned at saturation

Other 3BF and BHF variantsCompensation effects between stiffness

and Hyperon fraction

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

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 .

WAY OUT ?1. Some additional repulsion is presentfor 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 learnedsome fundamental properties of high density EOS

HOWEVER ………

Aaaaah !

3030

2.7 !!!!