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

Hyperon puzzle ! ? Massive (2M☉) neutron stars Softening of EOS by hyperon mixing 2010 PSR J1614-2230　(1.97±0.04)M☉ ? 2013 PSR J0348-0432　(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)

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

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

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)

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

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

E/A curves K value(MeV) MPa+ 313 MPa 283 MPb 254 4-body repulsion MPa/MPa+ including 3- and 4-body MPP : MPb including 3-body MPP only

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

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)

with n+p β-stable matter by solving TOV eq. with n+p β-stable matter 4-body repulsion K value(MeV) MPa+ 313 MPa 283 MPb 254 No ad hoc parameter to adjust stiffness of EOS besed on terrestrial data only except gP(4)/gP(3) ratio

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

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.

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

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

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

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

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)

Harada’s talk EΣ 0 100 200

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

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

Energy density

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

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

in spite of softening of EOS, 2Msolar is still obtained PSR J1614-2230　 Maximum mass for MPb (no 4-body repulsion) is less than 2Msolar

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

ΞN interaction and Ξ- mixing in neutron-star matter

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

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

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

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

Ξ- mixing

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-

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

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’