2015/8/4 JPARC ΞN interaction and Ξhypernuclei 1. ESC08c model and Kiso event (long history) 2. Ξ- mixing in neutron star (extremely large hypernucleus) Y. Yamamoto 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) BB相互作用模型 Nijmegen(from 197x) ハイパー核とYN相互作用 観点(1990) Baryon octet Meson nonet PS mesons SU(3) invariant Yukawa interaction independent constants goct, gsin, 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: g8, g1, α, θ 4×4=16 parameters for pseudo-scalar mesons vector mesons (two terms) scalar mesons & hard-core radii 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 Features of ND giving attractive UΞ * special modeling for scalar mesons * σ meson dominant attraction (universal in all channels) * Wigner type (weak exchange interaction) 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 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UΞの模型構築が 極めて困難であったことである Long history to find mechanism of attractive UΞ in ESC modeli quite difficult Long history ～25 years !!! Quark-core and UΣ / UΞ problem UΣ Experimentally repulsive NSC89/97 attractive ESC04a strongly attractive ESC04d strongly attractive ESC08a/b ESC08c UΞ weakly attractive strongly repulsive weakly attractive strongly attractive strongly repulsive strongly attractive moderately repulsive weakly attractive Quark-core effect Ξ-hypernuclei and ΞN interaction in emulsion no Ξ- can be seen 有史以前のデータ Mondal, et al., Nuovo Cimento 54 (1979) 333 UWS=-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！ UWS ??? P.T.P. Suppl.117 (1994) Y.Yamamoto, T.Motoba, T.Fukuda, M.Takahashi, K.Ikeda UWS=-24, -16, -12, -8 MeV D.J.Millener, C.B.Dover, A.Gal neglect UWS=-24 MeV E885 T. Fukuda , et al., Phys. Rev. C58 (1998), 1306. P.~Khaustov et al., Phys. Rev. C61 (2000), 054603 UWS=-14 MeV. Twin E176 1993 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; kF) G-matrix interactions Averaged-kF Approximation calculated self-consistently Mixed density obtained from SkHF w.f. 横浜イベント Recent : 0.82 +- 0.17 MeV prediction 木曽イベント !!!!! WS pot (-18.3) 1S 8.00 2P 0.82 Ehime 5.10 0.82 1S 9.21 5.45 2P 1.61 1.17 E176 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) ΞNのみ調節する パラメータはない ●Two-meson exchange processes are treated explicitly ● Meson-Baryon coupling constants are taken consistently with Quark-Pair Creation model repulsive cores spin singlet spin triplet Why is UΞ so attractive ? It’s due to tensor force as well as NN and ΛN-ΣN S12=0 . T=0 3S1 : ΞN T=1 3S1 : ΞN-ΛΣ-ΣΣ existence of S=-2 deuteron UΛ (T=1/2 3S1) -21.2 +18.9 : 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 ESC08c(ΞN)は適切な 引力を与える EXP (K-,K+) reactions lead to neutron-rich systems from available targets Various Ξ- nuclear bound states are produced by (K-,K+) rea 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 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 2P-Ξ- absorption scenario 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 2pΞ sΛpΛ double-Λ sticking 3dΞ pΛpΛ pΛpΛ 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 ? Hyperon puzzle ! Massive (2M☉) neutron stars 2010 PSR J1614-2230 (1.97±0.04)M☉ ? 2013 PSR J0348-0432 (2.01±0.04)M☉ Softening of EOS by hyperon mixing Our conclusion : The puzzle can be solved by Universal Three-Baryon Repulsion on the basis of terrestrial data RMF ours Lagrangian in Baryon-Meson system Bridge from “micro” to “macro” RＭF adjustable parameters interaction models two + three-body NN・YN scatteri Many-body pheno Earth-based experiments no parameter as possible Nuclear saturation properties EOS in neutron-star matter Based on BHF theory Our story to neutron-star matter starts from the BB interaction model Nijmegen Extended Soft-Core Model (ESC) SU3 invariant (NN and YN) interaction repulsive cores gP 2-body repulsion Naturally extended g3P SU3 scalar universal repulsio Pomeron is a model for multi-gluon exchange A model of Universal Three-Baryon Repulsion Multi-Pomeron Exchange Potential (MPP) The same repulsions in all baryonic channels NNN, NNY 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 but, essential is MPP for Nucleus-Nucleus density-dependent two-body attraction scattering data Three parameter sets 4-body How to determine coupling constants g3P and g4P ? Nucleus-Nucleus scattering data with G-matrix folding potential Double Folding U (R ) 1 (r1 ) 2 (r2 )vD (s; , E )dr1dr2 K s 1 (r1 , r1 s) 2 (r2 , r2 s)vEX (s; , E ) exp i dr1dr2 M VDFM (R ) iWDFM (R ) Frozen-Density Approximation ρ=ρ1+ρ2 Two Fermi-spheres separated in momentum space r 1 can overlap in coordinate space without disturbance of Pauli principle vNN(s) r2 16O + 16O elastic scattering cross section at E/A = 70 MeV 10 real part 10 -2 d /d -200 0 W (MeV) 0 -100 Ruth. V (MeV) 0 ESC Solid MPa Dashed MPa+ Dotted MPb -50 10 -100 0 -4 imaginary part 5 R (fm) 10 0 10 c.m. 20 (degree) Planned experiments (Tanihata et al.) : 12C+12C@E/A=200, 300, 400 MeV 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 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 Hyperon-Mixed Neutron-Star Matter using YN & YY interaction model ESC08c MPP TBA consistent with almost all experimental data of hypernuclei (S=-1,-2) universal in all BB channels given in S=0 channel ? in S=-1,-2 channel (ESC+MPP+TBA) model should be tested in hypernuclei hyperonic sector Choosing TBA=TNA Experimental data of BΛ reproduced G-matrix folding model no adjustable parameter MPa is better than ESC !!! 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 MPP & TBA cancel with each o around normal density region features of ESC remain Ξ- bound state (Kiso event in emulsion) 28Si (π-,K+) strength function UΞ=1.5 MeVのG-matrix folding potentialが UΞ=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) EoS of n+p+Λ+Σ+e+μ system ESC(YN) + MPP(YNN) +TBA(YNN) Energy density Hyperon-mixed neutron-star matter Λ Σ- 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 Ξ- mixing Maximum mass is not changed by Ξ- mixing Conclusion 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
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