1. Hyperon mixing and universal many-body repulsion in neutron stars
Y. Yamamoto
Collaborators:
T. Furumoto
N. Yasutake
Th.A. Rijken

2. Hyperon puzzle ! ? Massive (2M☉) neutron stars
Softening of EOS by hyperon mixing
PSR J 　(1.97±0.04)M☉ ?
PSR J 　(2.01±0.04)M☉
Aim of this talk :
We try to solve the puzzle by
Universal Three-Baryon Repulsion
on the basis of terrestrial experiments
Idea of Universal TBR by Takatsuka (2002)

3. strategy interaction models QCD: qurks+gluons
Bridge from “micro” to “macro”
interaction models
2-, 3-, 4-body
NN・YN scattering
Many-body phenom.
strategy
Earth-based experiments
no parameter as possible
Nuclear saturation properties
EOS in neutron-star matter
Based on BHF theory

4. Nijmegen Extended Soft-Core Model (ESC)
Our story to neutron-star matter
starts from the BB interaction model
Rijken’s talk
Nijmegen Extended Soft-Core Model (ESC)
SU3 invariant (NN and YN) interaction
repulsive cores

5. A model of Universal Many-Baryon Repulsion
Multi-Pomeron Exchange Potential (MPP)
Same repulsions in all baryonic channels NNN, NNY, NYY, YYY
Pomeron exchange propagator
is positive to give X-sections
at high energy
Then, low energy extrapolation
gives repulsive potential
two-gluon model
Effective two-body potential
from MPP (3- & 4-body potentials)

6. Three-Nucleon attraction (TNA) phenomenological
Both MPP and TNA are needed
to reproduce nuclear saturation property
(essential is MPP for Nucleus-Nucleus scattering data)
density-dependent two-body attraction
two parameters

7. Three parameter sets 4-body
to reproduce saturation property and nucleus-nucleus scattering data
4-body
MPP
TNA
rough estimation r
Kaidalov et al., N.P. B75(1974) 471

8. E/A curves
K value(MeV)
MPa
MPa
MPb
4-body
repulsion
MPa/MPa+ including 3- and 4-body MPP : MPb including 3-body MPP only

9. To determine coupling constants g3P and g4P
Nucleus-Nucleus scattering data
with G-matrix folding potential
Double Folding
Frozen-Density Approximation ρ=ρ1+ρ2 r2
Two Fermi-spheres separated in momentum space
can overlap in coordinate space without
disturbance of Pauli principle
vNN(s) r1

10. 16O + 16O elastic scattering cross section at E/A = 70 MeV
ESC
Solid MPa
Dashed MPa+
Dotted MPb
MPP
Angular distribution is reproduced owing to MPP contribution (TNA minor)

11. with n+p β-stable matter
by solving TOV eq.
with n+p β-stable matter
4-body repulsion
K value(MeV)
MPa
MPa
MPb
No ad hoc parameter to adjust stiffness of EOS
besed on terrestrial data only except gP(4)/gP(3) ratio

12. Hyperon-Mixed Neutron-Star Matter using YN & YY interaction model
ESC08c consistent with almost all experimental data
of hypernuclei (S=-1,-2)
MPP universal in all BB channels
TBA given in S=0 channel  ? in S=-1,-2 channels
(ESC+MPP+TBA) model should be tested in hypernuclei
hyperonic sector
to reproduce hypernuclear data
as possible as reasonably
Choosing TBA part

13. Y-nucleus folding potential derived from YN G-matrix interaction G(r; kF)
G-matrix interactions
Averaged-kF Approximation
calculated
self-consistently
Mixed density
obtained from SkHF w.f.

14. A single Λ in symmetric nuclear matter
similar
TBA=TNA cancels MPP repulsion at normal-density region
fine tuning
by G-matrix folding model
Strength of TBA is determined so as to reproduce the data
only one parameter

15. G-matrix folding model
with only one adjustable parameter : strength of TBA
MPa
ESC
Existence of
TBF effect

16. No adjustable parameter
for MPa
Isaka’s talk
Thursday
deformation
of cores
No adjustable parameter
Missing link of
accurate data

17. Using (ESC+MPP+TBA) model
MPP: universal in all BB channels
TBA: strength is only one parameter
Values of BΛ can be reproduced by order <0.5 MeV
(TBA part can be determined precisely)
Precise data of BΛ(A>16) at JLab are highly expected !!
missing link

18. A single Σ in symmetric nuclear matter
Quark Pauli effect
w/o TBA
MPa
ESC
In RMF approach
UΣ = +20 MeV usually
Chosen TBA(ΣN)=TBA(ΛN)

19. Harada’s talk EΣ

20. UΣ(EΣ) WΣ(EΣ) Potential for Σ with positive energy in nuclear matter
derived from G-matrix calculation
w/o TBA
UΣ(EΣ)
Σ potential for MPa is
strongly repulsive in
high energy region of EΣ
MPa
ESC
WΣ(EΣ)
similar
WS potential

21. EoS of n+p+Λ+Σ+e+μ system
Our ΛN & ΣN interactions (ESC08c+MPP+TBA)
are consistent with experimental data
Hyperon mixed neutron-star matter
EoS of n+p+Λ+Σ+e+μ system

22. Energy density

24. Onset density of Σ- is less than Λ !!
composition
Onset density of Σ- is less than Λ !!
(our ΣN interaction is not extremely repulsive)

25. Hyperon-mixed neutron-star matter
Λ Σ-
w/o Y mixing
Softening of EOS
by hyperon mixing

26. in spite of softening of EOS, 2Msolar is still obtained
PSR J 　
Maximum mass for MPb (no 4-body repulsion) is less than 2Msolar

27. Hyperon mixing
Softening of EOS by Y-mixing is of large effect
Hyperon puzzle (existence of 2Msolar) is a quantitative problem

28. ΞN interaction and Ξ- mixing in neutron-star matter

29. A single Ξ in nuclear matter with ESC08c
spin singlet
spin triplet

30. Emulsion events of twin Λ-hypernuclei
KEK-E176
Kiso event
KEK-E373
Uniquely
identified !

31. G-matrix folding model model
ESC08c(ΞN) gives
reasonable attraction
exp.
0.82
EXP
3.87
1.51
1.46
0.80
0.60
JLab

32. ESC+MPP+TBA Reproducing all features in S=0,-1,-2 systems consistently
s.p. potentials for MPa in neutron matter
ρY/ρn=0.1

33. Ξ- mixing

34. Maximum mass is not changed by Ξ- mixing (dashed curves)
For MPa case
w/o Y mixing
Maximum mass is not changed by Ξ- mixing (dashed curves)
because of universal MPP for Λ, Σ-, Ξ-

35. Summary ESC+MPP+TBA model
* MPP strength determined by analysis for 16O+16O scattering
* TNA adjusted phenomenologically to reproduce
saturation properties
* Consistent with hypernuclear data
* No ad hoc parameter to stiffen EOS
MPa/MPa+ set including 3- and 4-body repulsions
leads to massive neutron stars with 2M☉ in spite
of significant softening of EOS by hyperon mixing
MPb including 3-body repulsion leads to slightly smaller
value than 2M☉ quantitatively
Ξ- mixing does not change the maximum mass
when (MPP+TBA) is added to ΞN interaction

36. At least, one of solutions for ‘Hyperon Puzzle’
Concluding remark
Our interaction model (ESC08c+MPP+TBA)
is constrained by terrestrial experiments
assuming universal many-body repulsion
An upper limit of neutron-star masses is around 2M☉
(within 3- & 4-body pomeron exchange model)
No ad hoc parameter to stiffen EOS
At least, one of solutions for ‘Hyperon Puzzle’