K - 中間子原子核研究の現状 1.Introduction Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological K bar N potential 2.Variational calculation of K - pp with a chiral SU(3)- based K bar N potential 3.Recent status of the study of K - pp Theoretical side Experimental side 4.Summary and future plan Akinobu Doté (IPNS/KEK) Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN) T. Hyodo (TITech), W. Weise (TU Munich) JAEA seminar JAEA, Tokai, Japan Prototype of kaonic nuclei “K - pp” Prototype of kaonic nuclei “K - pp”

1. Introduction

Expanding the nuclear world 原子核 ＝ 陽子・中性子からなる有限量子多体系 、 安定核 … 約３００種 Large isospin 不安定核 … 約 3000 種、 RIBF ＠理研で展開 不安定核 … 約 3000 種、 RIBF ＠理研で展開

Expanding the nuclear world 原子核 ＝ 陽子・中性子からなる有限量子多体系 、 安定核 … 約３００種 Large isospin 不安定核 … 約 3000 種、 RIBF ＠理研で展開 不安定核 … 約 3000 種、 RIBF ＠理研で展開 Strangeness ハイパー核 … J-PARC (JAEA+KEK) で展開 ハイパー核 … J-PARC (JAEA+KEK) で展開

Kaonic nuclei Another form of nuclear system with strangeness K-K- Nucleus containing K - meson

Leading actors Key person Actors in K bar nuclei Supporting players Excited state of Λ 940p,n 1115 Λ 1190 Σ p + K Λ(1405) Λ + π Σ + π 1325 Energy [MeV] 940p,n 1115 Λ 1190 Σ p + K Λ(1405) Λ + π Σ + π 1325 Energy [MeV] I=0 Proton-K - bound state with 30MeV binding energy? with 30MeV binding energy? Not 3 quark state? Not 3 quark state? ← can’t be explained with a simple quark model… I=0 Proton-K - bound state with 30MeV binding energy? with 30MeV binding energy? Not 3 quark state? Not 3 quark state? ← can’t be explained with a simple quark model…

Leading actors Key person Actors in K bar nuclei Supporting players Excited state of Λ 940p,n 1115 Λ 1190 Σ p + K Λ(1405) Λ + π Σ + π 1325 Energy [MeV] Σπ channel is open at about 100 MeV below the Proton-K - threshold. Σπ channel is open at about 100 MeV below the Proton-K - threshold.

What is Kaonic nucleus? KNNN… ΣπNN… K nuclear state Deeply bound below πΣ threshold (main decay channel) Possible to exist as a quasi-bound state with narrow width Kaonic nucleus K-K- Bound by strong interaction Inside of nucleus The nuclear structure may be changed, if the interaction is so attractive.

1.free K bar N scattering data 2.1s level shift of kaonic hydrogen atom 3.binding energy and width of Λ(1405) Phenomenological K bar N potential (AY K bar N potential) Strongly attractive Y. Akaishi and T. Yamazaki, PRC 52, (2002) Λ(1405) = I=0 K - p quasi-bound state with 27 MeV binding energy Λ(1405) = I=0 K - p quasi-bound state with 27 MeV binding energy Studies with a phenomenological K bar N potential A. Doté, H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, (2004) Systematic study of various light kaonic nuclei ( 3 HeK - to 11 CK - ) with AMD + G-matrix (effective NN potential ) + AY K bar N potential shows their interesting properties… By a calculation of a few kaonic nuclei with a simple model, 3 HeK - turns out to be deeply bound by 100MeV with a narrow width of 20MeV. Deeply bound kaonic nuclei !

① Deeply bound and Dense ③ Isovector deformation ④ proton satellite pppK - ② Drastic change of structure 8 Be 8 BeK -

Theoretical studies of nuclear system with anti-kaons Medium to heavy nuclei with multi-antikaons Nuclear matter with antikoans Neutron star, kaon condensation… - T. Muto, T. Maruyama and T. Tatsumi, PRC79, (2009) - D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, (2007); PRC77, (2008) Light nuclei with a single antikaon 3 HeK - ～ 11 CK - studied with AMD + G-matrix + AY potential E(K) ≒ 100MeV Light nuclei with double antikaons 3 HeK - K - etc studied with AMD + G-matrix + AY potential E(2K) ≒ 200MeV Studied with Relativistic Mean Field … Antikaon part is based on non-linear chiral Lagrangian Strongly repulsive K bar K bar interaction Saturation for the number of antikaons In case of 15 O+xK -, central nuclear density and –B/x are saturated for x>8.

2. Variational calculation of K - pp with a chiral SU(3)- based K bar N potential

Are kaonic nuclei really exotic? The phenomenological K bar N potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. K bar NπΣηΛKΞ Chiral SU(3) AY potential

The phenomenological K bar N potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed?? Are kaonic nuclei really exotic?

More theoretical study of the most essential kaonic nucleus K - pp system “Prototype of kaonic nuclei” studied with a chiral SU(3)-based K bar N potential

Variational calculation of K - pp with a chiral SU(3)-based K bar N potential with a chiral SU(3)-based K bar N potential Av18 NN potential Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) 1E1E 1E1E Strong repulsive core (3 GeV) Strong repulsive core (3 GeV)

Variational calculation of K - pp with a chiral SU(3)-based K bar N potential with a chiral SU(3)-based K bar N potential Av18 NN potential Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective K bar N potential based on Chiral SU(3) theory Effective K bar N potential based on Chiral SU(3) theory … reproduce the original K bar N scattering amplitude obtained with coupled channel chiral dynamics. with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential Single channel, Energy dependent, Complex, Gaussian-shape potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009)

Local K bar N potential based on Chiral SU(3) I=0 K bar N scattering amplitude Chiral unitary; T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, (2003) Chiral Unitary 1420 Resonance position in I=0 K bar N channel In Chiral unitary model, 1420 MeV not 1405 MeV ! Effective potential T. Hyodo and W. Weise, PRC77, (2008)

Variational calculation of K - pp with a chiral SU(3)-based K bar N potential with a chiral SU(3)-based K bar N potential Av18 NN potential Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective K bar N potential based on Chiral SU(3) theory Effective K bar N potential based on Chiral SU(3) theory … reproduce the original K bar N scattering amplitude obtained with coupled channel chiral dynamics. with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential Single channel, Energy dependent, Complex, Gaussian-shape potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) I=0 K bar N resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV I=0 K bar N resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV Variational method Variational method … Trial wave function contains NN/K bar N correlation functions. The NN repulsive core can directly be treated. NN K bar

Variational calculation of K - pp with a chiral SU(3)-based K bar N potential with a chiral SU(3)-based K bar N potential Av18 NN potential Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). Effective K bar N potential based on Chiral SU(3) theory Effective K bar N potential based on Chiral SU(3) theory … reproduce the original K bar N scattering amplitude obtained with coupled channel chiral dynamics. with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential Single channel, Energy dependent, Complex, Gaussian-shape potential Four variants of chiral unitary modes × Total B. E. : 20 ± 3 MeV  （ K bar N→  Y ） : 40 ～ 70 MeV Total B. E. : 20 ± 3 MeV  （ K bar N→  Y ） : 40 ～ 70 MeV Shallow binding and large decay width A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) I=0 K bar N resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV I=0 K bar N resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV Variational method Variational method … Trial wave function contains NN/K bar N correlation functions. The NN repulsive core can directly be treated.

Structure of K - pp NN K bar

Structure of K - pp K bar 2.21 fm 1.97 fm NN Cf) NN distance in normal nuclei ～ 2 fm Size of deuteron ～ 4 fm

Structure of K - pp K bar NN Mixture of T N =0 component = 3.8 % NN distance = 2.21 fm K bar N distance = 1.97 fm 1.97 fm

Structure of K - pp K bar NN Mixture of T N =0 component = 3.8 % I=0 K bar N 1.82 fm NN distance = 2.21 fm K bar N distance = 1.97 fm

Structure of K - pp K bar NN Mixture of T N =0 component = 3.8 % I=0 K bar NI=1 K bar N 1.82 fm2.33 fm NN distance = 2.21 fm K bar N distance = 1.97 fm

Structure of K - pp N Mixture of T N =0 component = 3.8 % I=0 K bar NI=1 K bar N 1.82 fm2.33 fm NN distance = 2.21 fm K bar N distance = 1.97 fm “Λ(1405)” as I=0 K bar N calculated with this potential 1.86 fm K bar N Almost “Λ(1405)”

Structure of K - pp Density distribution: K bar N pair in K - pp vs “  (1405)” N K bar “Λ(1405)” Isospin 0 K bar N pair Isospin 0 K bar N pair Isospin 1 K bar N pair Isospin 1 K bar N pair N “K - pp ” Isospin 0 and 1 mixed N K bar “  (1405)” almost survives in K - pp!

Dispersive correction Dispersive correction (Effect of imaginary part) (Effect of imaginary part) +6 ～ +18 MeV p-wave K bar N potential p-wave K bar N potential ～ -3 MeV 10 ～ 35 MeV Two nucleon absorption Two nucleon absorption 4 ～ 12 MeV s-wave K bar N potential (Variational calculation) B.E.Width 20 ± 3 MeV 40 ～ 70 MeV Rough estimation 20 ～ 40 MeV Total B.E. 55 ～ 120 MeV Total Width K - pp … Very large… Variational calculation of K - pp with a chiral SU(3)-based K bar N potential with a chiral SU(3)-based K bar N potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009) A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, (2009)

3. Recent status of the study of kaonic nuclei Prototype of kaonic nuclei “K - pp”

K bar nuclei = Exotic system !? To make the situation more clear … K - pp= Prototye of K bar nuclei Studied with various methods, because it is a three-body system: Doté, Hyodo, Weise Variational with a chiral SU(3)-based K bar N potential PRC79, (2009) Akaishi, Yamazaki ATMS with a phenomenological K bar N potential PRC76, (2007) Ikeda, Sato Faddeev with a chiral SU(3)-derived K bar N potential PRC76, (2007) Shevchenko, Gal, Faddeev with a phenomenological K bar N potential PRC76, (2007) Mares Wycech, Green Variational with a phenomenological K bar N potential (with p-wave) PRC79, (2009) Arai, Yasui, Oka Λ* nuclei model PTP119, 103(2008) continued by Uchino, Hyodo, Oka Nishikawa, Kondo Skyrme model PRC77, (2008) All calculations predict that K - pp can be bound. Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN) Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti) There are several experiments:

Width (K bar NN→πYN) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Akaishi, Yamazaki [2] (Variational, Phenomenological) Akaishi, Yamazaki [2] (Variational, Phenomenological) Exp. : FNUDA [5] Exp. : DISTO [6] (Finalized) Exp. : DISTO [6] (Finalized) Using S-wave K bar N potential constrained by experimental data. … K bar N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [1] PRC79, (2009) [2] PRC76, (2007) [3] PRC76, (2007) [4] PRC76, (2007) [5] PRL94, (2005) [6] PRL104, (2010) Recent results of calculation of K - pp Recent results of calculation of K - pp and related experiments

Width (K bar NN→πYN) [MeV] Exp. : FNUDA [5] Exp. : DISTO [6] (Finalized) Exp. : DISTO [6] (Finalized) Using S-wave K bar N potential constrained by experimental data. … K bar N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [1] PRC79, (2009) [2] PRC76, (2007) [3] PRC76, (2007) [4] PRC76, (2007) [5] PRL94, (2005) [6] PRL104, (2010) Recent results of calculation of K - pp Recent results of calculation of K - pp and related experiments Akaishi, Yamazaki [2] (Variational, Phenomenological) Akaishi, Yamazaki [2] (Variational, Phenomenological) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Wycech, Green [7] (Variational, phenomenological, P-wave) Wycech, Green [7] (Variational, phenomenological, P-wave) [7] PRC79, (2009) Including P-wave K bar N potential, and other effects. Including P-wave K bar N potential, and other effects. Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Doté, Hyodo, Weise [1] (Variational, Chiral SU(3))

Recent results with various calculations of K - pp B. E.Γ (mesonic) Method K bar N Int. Channels at final step DHW 20 ± 3 40 ～ 70 Variational Chiral SU(3) K bar N AY Variational Phenom. K bar N IS 60 ～ ～ 80 Faddeev Chiral SU(3) K bar N, πY (AGS) (Separable) SGM 50 ～ ～ 110 Faddeev Phenom. K bar N, πY (AGS) (Separable) Exp. FINUDA 115±7 67±14 K - absorption, Λp inv. mass DISTO 103±3±5 118±8±10 p+p→K + +Λ+p, Λp inv. mass (Finalized) All four calculations shown above are constrained by experimental data. … K bar N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave K bar N potential is used.

Recent results with various calculations of K - pp B. E.Γ (mesonic) Method K bar N Int. Channels at final step DHW 20 ± 3 40 ～ 70 Variational Chiral SU(3) K bar N AY Variational Phenom. K bar N IS 60 ～ ～ 80 Faddeev Chiral SU(3) K bar N, πY (AGS) (Separable) SGM 50 ～ ～ 110 Faddeev Phenom. K bar N, πY (AGS) (Separable) DHW vs AY Difference of the used K bar N interactions.

Comparison of AY potential and Chiral-based potential AY potential Weinberg-Tomozawa term derived from Chiral SU(3) effective Lagrangian K bar NπΣηΛKΞ Coupled channel Chiral dynamics Energy independent potential No πΣ-πΣ interaction Energy dependent potential Somewhat strongly attractive πΣ-πΣ interaction Λ(1405) = a quasi-bound state of I=0 K bar N at 1405MeV. Appears in I=0 K bar N channel. I=0 K bar N 1405MeV. Λ(1405) = a quasi-bound state of I=0 K bar N at 1405MeV. Appears in I=0 K bar N channel. I=0 K bar N 1405MeV. Two poles (double pole); one couples strongly to K bar N, the other couples strongly to πΣ. Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣ channel. I=0 K bar N 1420MeV. Two poles (double pole); one couples strongly to K bar N, the other couples strongly to πΣ. Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣ channel. I=0 K bar N 1420MeV.

I=0 K bar N full scattering amplitude Almost same in the on-shell region Quite different in the sub-threhold region Comparison of AY potential and Chiral-based potential

Recent results with various calculations of K - pp B. E.Γ (mesonic) Method K bar N Int. Channels at final step DHW 20 ± 3 40 ～ 70 Variational Chiral SU(3) K bar N AY Variational Phenom. K bar N IS 60 ～ ～ 80 Faddeev Chiral SU(3) K bar N, πY (AGS) (Separable) SGM 50 ～ ～ 110 Faddeev Phenom. K bar N, πY (AGS) (Separable) DHW vs AY In Chiral SU(3) theory, the πΣ-πΣ interaction is so attractive to make a resonance, while AY potential doesn’t have it. “Λ(1405)” is I=0 K bar N bound state at 1420 MeV or 1405 MeV? AY potential is twice more attractive than Chiral-based one.

Recent results with various calculations of K - pp B. E.Γ (mesonic) Method K bar N Int. Channels at final step DHW 20 ± 3 40 ～ 70 Variational Chiral SU(3) K bar N AY Variational Phenom. K bar N IS 60 ～ ～ 80 Faddeev Chiral SU(3) K bar N, πY (AGS) (Separable) SGM 50 ～ ～ 110 Faddeev Phenom. K bar N, πY (AGS) (Separable) DHW vs IS Separable approximation? Different energy dependence of interaction kernel V ij ? πΣN three-body dynamics … may not be included in DHW. (Y. Ikeda and T. Sato, PRC79, (2009)) Although both are based on Chiral SU(3) theory, results are very different from each other.

Variational cal. vs Faddeev The K bar N potentials used in both calculations are constrained with Chiral SU(3) theory, but … Total B. E. = 20±3 MeV, Decay width = 40 ～ 70 MeV A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, (2009) Variational calculation (DHW) Variational calculation (DHW) Faddeev calculation (IS) Faddeev calculation (IS) Total B. E. = 60 ～ 95 MeV, Decay width = 45 ～ 80 MeV Y. Ikeda, and T. Sato, Phys. Rev. C76, (2007) ? ? ? Discrepancy between Variational calc. and Faddeev calc. Separable potential used in Faddeev calculation? Non-relativistic (semi-relativistic) vs relativistic? Energy dependence of two-body system (K bar N) in the three-body system (K bar NN)? …??? Why ?

Variational cal. vs Faddeev The K bar N potentials used in both calculations are constrained with Chiral SU(3) theory, but … Total B. E. = 20±3 MeV, Decay width = 40 ～ 70 MeV A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, (2009) Variational calculation (DHW) Variational calculation (DHW) Faddeev calculation (IS) Faddeev calculation (IS) Total B. E. = 60 ～ 95 MeV, Decay width = 45 ～ 80 MeV Y. Ikeda, and T. Sato, Phys. Rev. C76, (2007) ? ? ? Discrepancy between Variational calc. and Faddeev calc. A possible reason is πΣN thee-body dynamics In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective K bar N potential. Y. Ikeda and T. Sato, PRC79, (2009)

Experiments related to K - pp

FINUDA collaboration (DAΦNE, Frascatti) Experiments related to K - pp K - absorption at rest on various nuclei ( 6 Li, 7 Li, 12 C, 27 Al, 51 V) Invariant-mass method Strong correlation between emitted p and Λ (back-to-back) Invariant mass of p and Λ K-K- p p p Λ If it is K - pp, … Total binding energy = 115 MeV Decay width = 67 MeV PRL 94, (2005)

Re-analysis of KEK-PS E549 DISTO collaboration - p + p -> K + + Λ GeV - Λp invariant mass - Comparison with simulation data T. Yamazaki et al. (DISTIO collaboration), PRL104, (2010) - K - stopped on 4 He target - Λp invariant mass T. Suzuki et al (KEK-PS E549 collaboration), arXiv: v1[nucl-ex] K - pp??? B. E.= 103 ±3 ±5 MeV Γ = 118 ±8 ±10 MeV K - pp??? B. E.= 103 ±3 ±5 MeV Γ = 118 ±8 ±10 MeV Strong Λp back-to-back correlation is confirmed. Unknown strength is there in the same energy region as FINUDA. Strong Λp back-to-back correlation is confirmed. Unknown strength is there in the same energy region as FINUDA. Experiments related to K - pp

J-PARC will give us lots of interesting data! E15: A search for deeply bound kaonic nuclear states by 3 He(inflight K -, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) E17: Precision spectroscopy of kaonic 3 He atom 3d→2p X-rays --- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken) All emitted particles will be measured. Dr. Fujioka’s talk (KEK workshop, 7-9. Aug. 08)

4. Summary and future plan

4. Summary Kaonic nuclei are exotic system !? Variational calc. of K - pp with a chiral SU(3)-based K bar N pot. B. E. =20±3 MeV, Γ(K bar NN → πYN) = 40 – 70MeV With p-wave K bar N pot., dispersion correction, and two-nucleon absorption, B. E. =20 – 40 MeV, Γ = 55 – 120MeV AMD calculation with G-matrix method using a phenomenological K bar N potential (AY potential) shows that kaonic nuclei may have lots of interesting properties: Deeply bound and narrow width dense system with interesting structure… Kaonic nuclei are another form of nuclear system involving strangeness. They might be exotic system because of the strong attraction of I=0 K bar N potential. However, these properties have not been established and there are some questions. Two protons distance = 2.2fm ≒ NN mean distance of normal nucleus Λ(1405) structure (correlation) remains in K - pp. K - pp is a shallowly bound and not so dense system.

4. Summary Current status of studies of K - pp The most essential K bar nuclei “K - pp” (K bar NN, J p =1/2 -, T=0) has been investigated in various ways. But the situation is still controversial… Theory Variational + Phenom. K bar N B.E. = 47MeV, Γ= 61MeV PRC76, (2007) Variational + Chiral-based K bar N B.E. = 20±3MeV, Γ= 40 ～ 70MeV PRC79, (2009) Faddeev + Phenom. K bar N B.E. = 50 ～ 70MeV, Γ= ～ 100MeV PRC76, (2007) Faddeev + Chiral-based K bar N B.E. = 60 ～ 95MeV, Γ= 45 ～ 80MeV PRC76, (2007) Experiment (Unknown object which seems related to K - pp) FINUDA B.E. = 115MeV, Γ= 67MeV PRL94, (2005) DISTO B.E. = 103MeV, Γ= 118MeV PRL104, (2010) Discrepancy between theoretical studies of K - pp DHW (Variational with Chiral-based) vs AY (Variational with phenomenological) … Difference of K bar N attraction Λ(1420) scheme and Λ(1405) scheme DHW (Variational with Chiral-based) vs IS (Faddeev with Chiral-based) … πΣN three-body dynamics (might be also different energy dependence of interaction kernel? ) … if it is K - pp

4. Future plan What is the object measured experimentally? A bound state of K - pp, or another object such as πΣN ??? Only what we can say from only this spectrum is “There is some object with B=2, S=-1, charge=+1”… Since the signal position is very close to π+Σ+N threshold, the πΣN degree seems important in the observed state. As pointed out by Dr. Ikeda and Prof.Sato, the πΣN dynamics may be important. (especially, in case that K - pp is deeply bound???) Direct treatment of πΣN degree, dealing with a resonant state, based on variational scheme. Coupled channel Complex Scaling

Thank you for your attention!