ΞN interaction and Ξhypernuclei 1.ESC08c model and Kiso event (long history) 2.Ξ - mixing in neutron star (extremely large hypernucleus) Y. Yamamoto 2015/8/4 JPARC

湯川理論 (1935) 坂田模型 (1955) pnΛ SU(3) 対称性 IOO 八道説 バリオンオクテット 武谷核力論 (1953) OBEP 斥力芯 ハイパー核発見 (1952) ハイパー核と YN 相互作用 観点 (1990) BB 相互作用模型 Nijmegen(from 197x)

Baryon octet Meson nonet PS mesons

SU(3) invariant Yukawa interaction independent constants g oct, g sin, α, (mixing angle θ)

以上は古い素粒子論の教科書に書いてある話 Parameter fitting for NN & YN scattering data Nijmegen group from 1970’s after that long long history to ESC08c

Parameters in ND/NF: g 8, g 1, α, θ 4×4=16 parameters for pseudo-scalar mesons vector mesons (two terms) scalar mesons & hard-core radii Nijmegen group Continuous Studies by Nijmegen group since 1970’s Parameter fitting with complementary use of (rich) NN and (scarce) YN scattering data

Special modeling in ND related to attractive ΞN interaction not taken

Hard Core model は最初の一歩、核力屋の練習台 Soft Core model==> 模型の構築 (ω, pomeron, QM, etc) ND は HC 故の現象論的性質（融通無碍） によって長々と生き延びたが もはや歴史博物館に収納 ND が長命になった理由の一つは引力的 U Ξ の模型構築が 極めて困難であったことである Features of ND giving attractive U Ξ * special modeling for scalar mesons * σ meson dominant attraction (universal in all channels) * Wigner type (weak exchange interaction) Long history to find mechanism of attractive U Ξ in ESC modeling quite difficult

Quark-core and U Σ / U Ξ problem U Σ U Ξ Experimentally repulsive weakly attractive NSC89/97 attractive strongly repulsive ESC04a strongly attractive weakly attractive ESC04d strongly attractive strongly attractive ESC08a/b strongly repulsive strongly attractive ESC08c moderately repulsive weakly attractive Quark-core effect Long history ～ 25 years !!!

Ξ-hypernuclei and ΞN interaction in emulsion

Mondal, et al., Nuovo Cimento 54 (1979) 333 有史以前のデータ no Ξ - can be seen

U WS =-24 MeV （有史以前のパラダイム）

E176 events of twin Λ hypernuclei Ξ - 吸収によるダブルストレンジネス・ エマルジョン実験の問題点 Ξ - がどの軌道から吸収されたか分からない 一般的にイベントはユニークに同定できな い Λ- or ΛΛ-fragments は励起状態であり得る 複数のイベント・解釈から consistent solution を見つけ る

Twin の最初のドラフトのタイトルは Ξ ハイパー核の生成 Atomic Ξ - cascade では 1S まで落ちない 2P

Coulomb -bound Coulomb -assisted

E176 events 2P 吸収で consistent understanding, but 3D 吸収の可能性は否定しきれない！

P.T.P. Suppl.117 (1994) Y.Yamamoto, T.Motoba, T.Fukuda, M.Takahashi, K.Ikeda U WS =-24, -16, -12, -8 MeV D.J.Millener, C.B.Dover, A.Gal U WS =-24 MeV E885 T. Fukuda, et al., Phys. Rev. C58 (1998), P.~Khaustov et al., Phys. Rev. C61 (2000), U WS =-14 MeV. U WS ??? Twin E neglect

Twin events を使った唯一の (?) 理論の論文

Y-nucleus folding potential derived from YN G-matrix interaction G(r; k F ) Averaged-k F Approximation G-matrix interactions Mixed densityobtained from SkHF w.f. calculated self-consistently

横浜イベント 木曽イベント !!!!! prediction Recent : MeV

WS pot (-18.3) Ehime 1S P E176 1S P Kiso event WS potential の予言性は低い

KISO event

木曽イベント Some possibilities

Extended Soft-Core Model (ESC) ●Two-meson exchange processes are treated explicitly ● Meson-Baryon coupling constants are taken consistently with Quark-Pair Creation model repulsive cores ΞN のみ調節する パラメータはない

spin singlet spin triplet

. S 12 =0 Why is U Ξ so attractive ? It’s due to tensor force T=0 3 S 1 : ΞN T=1 3 S 1 : ΞN-ΛΣ-ΣΣ existence of S=-2 deuteron as well as NN and ΛN-ΣN U Λ (T=1/2 3 S 1 ) : ΛN-ΣN tensor 1.56 MeV

Origin of strong tensor force in ESC08c π exchange (ΞN-ΞN) K exchange (ΞN-ΛΣ) Vector & Axial vector exchange Meson-pair exchange

G-matrix folding model model EXP ESC08c(ΞN) は適切な 引力を与える

Various Ξ - nuclear bound states are produced by (K -,K + ) reactions ! (K -,K + ) reactions lead to neutron-rich systems from available targets

Cascade calculation  dominantly from 3d and 4f a few % from 2p by Koike & Akaishi なぜ 2P Ξ - bound states ばかり見つかるのか？

Ξ - 吸収によるダブルストレンジネス・エマルジョン実験 ＊ Ξ - がどの軌道から吸収されたか分からない ＊一般的にイベントはユニークに同定できない ＊ Λ- or ΛΛ-fragments は励起状態であり得る 2P-Ξ - absorption scenario 複数のイベント・解釈から consistent solution を見つける a consistent solution from some interpretations of events

Deep hole state  cancelling of Δ

double-Λ sticking

2p- 吸収による double-Λ sticking の確率は 3d- 吸収の 3 倍

Double-Λ sticking from Ξ-absorption through s-hole process 2p Ξ  s Λ p Λ  double-Λ sticking 3d Ξ  p Λ p Λ p Λ p Λ sticking state から double-Λ fragment や twin Λ fragments への 崩壊確率は小さいであろう

Hyperon mixing in neutron-star matter Ξ - mixing ?

Massive (2M ☉ ) neutron stars Softening of EOS by hyperon mixing Hyperon puzzle ! Our conclusion : The puzzle can be solved by Universal Three-Baryon Repulsion on the basis of terrestrial data 2010 PSR J (1.97±0.04)M ☉ 2013 PSR J (2.01±0.04)M ☉ ?

Lagrangian in Baryon-Meson system interaction models two + three-body NN ・ YN scattering Many-body phenom. Nuclear saturation properties EOS in neutron-star matter RＭFRＭF no parameter as possible adjustable parameters RMF ours Earth-based experiments Based on BHF theory Bridge from “micro” to “macro”

Nijmegen Extended Soft-Core Model (ESC) repulsive cores Our story to neutron-star matter starts from the BB interaction model SU 3 invariant (NN and YN) interaction

SU 3 scalar universal repulsion Pomeron is a model for multi-gluon exchange gPgP g 3P Naturally extended 2-body repulsion

Multi-Pomeron Exchange Potential (MPP) The same repulsions in all baryonic channels NNN, NNY, NYY, YYY A model of Universal Three-Baryon Repulsion Three-Nucleon attraction (TNA) phenomenological Both MPP and TNA are needed to reproduce nuclear saturation property but, essential is MPP for Nucleus-Nucleus scattering data Effective two-body potential from MPP (3- & 4-body potentials) density-dependent two-body attraction

Three parameter sets 4-body

How to determine coupling constants g 3P and g 4P ? Nucleus-Nucleus scattering data with G-matrix folding potential r1r1 r2r2 v NN (s) Double Folding Frozen-Density Approximation ρ=ρ 1 +ρ 2 Two Fermi-spheres separated in momentum space can overlap in coordinate space without disturbance of Pauli principle

16 O + 16 O elastic scattering cross section at E/A = 70 MeV Solid MPa Dashed MPa + Dotted MPb ESC Planned experiments (Tanihata et al.) : 12 C , 400 MeV

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

No ad hoc parameter to adjust stiffness of EOS by solving TOV eq. K value(MeV) MPa MPa 283 MPb 254 with n+p β-stable matter 4-body repulsion

Hyperon-Mixed Neutron-Star Matter using YN & YY interaction model ESC08c ESC08c consistent with almost all experimental data of hypernuclei (S=-1,-2) MPP MPP universal in all BB channels TBA TBA given in S=0 channel  ? in S=-1,-2 channel (ESC+MPP+TBA) model should be tested in hypernuclei hyperonic sector Experimental data of B Λ reproduced Choosing TBA=TNA

MPa is better than ESC !!! no adjustable parameter G-matrix folding model Existence of three-body force effect

ESC Reproducing all features in S=0,-1,-2 systems consistently s.p. potentials for MPa in neutron matter Ξ - bound state (Kiso event in emulsion) MPP & TBA cancel with each other around normal density region features of ESC remain

28 Si (π -,K + ) strength function U Ξ =1.5 MeV の G-matrix folding potential が U Ξ =20-30 MeV の Woods-Saxon potential と似た結果を与える

Hyperon-mixed Neutron-Star matter with universal TBR (MPP) ESC(YN) + MPP(YNN) +TBA(YNN) EoS of n+p+Λ+Σ+e+μ system

Energy density

Hyperon-mixed neutron-star matter Λ Σ-Λ Σ- Softening of EOS by hyperon mixing

PSR J Maximum mass for MPb (no 4-body repulsion) is less than 2M solar In spite of softening of EOS, 2M solar is still obtained

Ξ - mixing

Maximum mass is not changed by Ξ - mixing

Conclusion ESC+MPP+TBA model * MPP strength determined by analysis for 16 O+ 16 O 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