1. 1.Introduction 2.Exotic properties of K nuclei 3.Recent experimental results Strange tribaryons by KEK experiment ppK - by FINUDA ppnK - by FOPI 4.Future developments 5.Summary and future plans Exotic system: Kaonic nuclei the present status and the future development QCD とハドロン物理の新展開 @ KEK, ’06.Mar.1 A. Dote （ KEK ） Y. Akaishi (Nihon univ.) T. Yamazaki (RIKEN) ´

2. Introduction What are kaonic nuclei (K nuclei)? K - meson is bound in a nucleus by strong interaction. cf) Kaonic atom K - meson is around a nucleus, bound by Coulomb interaction. K nuclei can exist as discrete states, since K - meson is deeply bound below Σπ threshold. KNNN… ΣπNN… K nuclear state

3. Deeply bound; Binding energy of K - > 100 MeV Discrete state; Below Σπ threshold Very attractive I=0 KN interaction makes …... Deeply bound kaonic nuclei 1.free KN scattering data 2.1s level shift of kaonic hydrogen atom 3.binding energy and width of Λ(1405) Phenomenological KN potential (AY KN potential) Strongly attractive. Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 = K - + proton

4. My motivation Only one K - meson can drastically change the nuclear structure? Only one K - meson can drastically change the nuclear structure? Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 8 Be + K - … Akaishi’s special lecture held in Kyoto university in ’00.

5. Exotic features of K nuclei Fully microscopic treatment No assumption on nuclear structure; cluster, deformation … System self-organizes only following energy variation. p n Normal nucleus p n K-K- normal nucleus ? ?? ? ? ? Kaonic nucleus What kind of structure does A+1 system favor? A nti-symmetrized M olecular D ynamics

6. Essence of AMD Cooling 0s 0p Shell Cluster Gaussian wave packet AMD wave function can describe not only shell-model-like structure but also cluster-like one. The structure is determined by only the energy-variation. The structure is determined by only the energy-variation.

7. ☆ Improve AMD for K nuclei mixing + Charge projection of total wave function Single nucleon/kaon wave function

8. Hamiltonian in AMD calculation : effective NN int. Tamagaki potential (OPEG) : effective KN int. AY KN potential G-matrix method Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 We used only central potential as V NN before the discovery of strange tribaryons.

9. A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. AMD studies revealed … 1.E(K) > 100 MeV for various light nuclei 2.Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - 3.Highly dense state is formed in K nuclei. maximum density > 4ρ 0 averaged density 2 ～ 4ρ 0 4.Proton satellite in pppK - Rrms = 2.46 fm β = 0.63 Central density = 0.10 /fm^3 8 Be Density (/fm^3) 0.0 0.10 0.20 Nucleus-K - threshold Σπ threshold (simple AMD) Width (Σπ, Λπ) Rrms = 1.42 fm β = 0.55 Central density = 0.76 /fm^3 8 BeK - Density (/fm^3) 0.0 0.41 0.83 4.5 normal density Binding energy of K - = 104 MeV Isovector deformation pppK - Proton satellite

10. Various shapes of K nuclei ppnK - pppK - pppnK - 6 BeK - 3 fm 9BK-9BK- 4 fm 8.8ρ 0 9.2ρ 0 7.6ρ 0 5.4ρ 0 4.1ρ 0 1.141.67 1.78 2.552.53 4 fm 4.1ρ 0 Single K - meson can interact with limited numbers of nucleons? Saturation of E(K)

11. Recent experimental results T. Suzuki, M.Iwasaki et al; 4 He(stopped K -, n or p) @ KEK H. Fujioka, T. Nagae et al; ppK - @ DAΦNE Kishimoto et al; 16 O(inflight K -, n) 15 OK - @ BNL N.Herrmann et al; Invariant-mass method (heavy-ion collision) @ GSI K. Suzuki et al; proton induced reaction @ GSI J-PARC Various groups are trying to search for deeply bound kaonic nuclei in various way.

12. KEK group ppnK - (T=0) ppnK - (T=0) 4 He (stopped K -, n) ppnK - 4 He (stopped K -, p) pnnK - pnnK - (T=1) pnnK - (T=1) T. Suzuki, M. Iwasaki et al KEK Stopped K - reaction on 4He target Missing-mass method (Detecting p or n) ppnK - :Strange tribaryon S + (3140) arXiv: nucl-ex/0310018 Total binding energy = 169 MeV Decay width < 25 MeV pnnK - :Strange tribaryon S 0 (3115) PLB 597, 263 (2004) Total binding energy = 194 MeV Decay width < 21 MeV

13. FINUDA group H. Fujioka, T. Nagae et al e + e - collider DAΦNE, FINUDA spectrometer K - absorbtion at rest on various nuclei Invariant-mass method Strong correlation between emitted p and Λ (back-to-back) Invariant mass of p and Λ ppK - Total binding energy = 115 MeV Decay width = 67 MeV PRL 94, 212303 (2005)

14. FOPI group GSI Heavy-ion collision Ni+Ni @ 1.93 A GeV Invariant-mass method Invariant mass of d and Λ N. Herrmann et al ppnK - Total binding energy = ～ 150 MeV Decay width = 100 MeV ? Preliminary !

15. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK -

16. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK - Experimental results are more deeply bound than ours. Experimental results are more deeply bound than ours.

17. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK - Experimental results are more deeply bound than ours. Experimental results are more deeply bound than ours. 14% enhanced KN interaction NN-LS interaction is important in pnnK -. 14% enhanced KN interaction NN-LS interaction is important in pnnK -. B.E. = 177 MeV B.E. = 177 MeV B.E. = 187 MeV B.E. = 187 MeV J π =1/2 -, T=0 (0s) 3 J π =3/2 +, T=1 (0s) 2 (0p) Isobaric analog state of pppK - Large energy gain by KN interaction Additional energy gain by NN-LS interaction

18. Nucleon configuration of pnnK - I=0 KN I=1 KN 1 / 6 5 / 6 2 / 3 1 / 3 1 / 2 ppnK - pnnK - (0s) 3 (0s) 2 (0p) T=0 T=1 P n K- pn K-K- K0K0

19. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK - Decay width is consistent? Decay width is consistent?

20. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK - Consistent? Especially, decay width. Consistent? Especially, decay width.

21. Summary of present status Our predictions B.E. = 48 MeV Γ = 61 MeV B.E. = 118 MeV Γ = 21 MeV B.E. = 87 MeV Γ = 133 MeV KEK B.E. = 169 MeV Γ < 25 MeV B.E. = 194 MeV Γ < 21 MeV FINUDA B.E. =115 MeV Γ = 67 MeV FOPI B.E. ～ 150 MeV Γ ～ 100 MeV ppK - ppnK - pnnK - ??? Unobserved states can be found by each other experiment? Unobserved states can be found by each other experiment?

22. Future developments Theory 1, Short-range repulsive core part of NN interaction The repulsive core part of the effective NN potential derived by G-matrix method is too much smoothed out for the study of kaonic nuclei? “Beyond the conventional nuclear physics” 3, Mystery of two-body absorption (KNN --> YN) … large decay width at high density K nuclei can survive? 4, The study from the view point of quarks; Quark matter or not? 2, Using more theoretical KN interaction Energy- and density-dependence I=1 P-wave interaction … Attractive below Σ(1385). … Large contribution at high density? Additional attraction to deeply bound kaonic nuclei

23. Future developments Experiment 1, More experiments to confirm the existence of kaonic nuclei 2, Determine J π of, especially, strange tribaryons 3, Dense or not? Possible by measuring the momentum correlation of three particles emitted in the decay NNNK → N+N+Λ P. Kienle, Y. Akaishi and T. Yamazaki, Phys.Lett.B632, 187 (2006)

24. Summary  Kaonic nuclei have interesting properties! The AMD study with AY KN interaction showed … K - is deeply bound by ～ 100 MeV and forms highly dense state. Strange structures appear in K nuclei. Drastic change of 8 Be structure, Isovector deformation in 8 BeK -, Proton satellite in pppK -.  Observed strange tribaryons, ppnK - and pnnK -, can be understood … 14% enhanced KN interaction and NN-LS force pnnK - : (0s) 2 (0p) configuration J π =3/2 +, T=1 ppnK - : (0s) 3 configuration J π =1/2 -, T=0

25. Summary  Various experimental results are now reported. They indicate the evidence of deeply bound kaonic nuclei. But comparing with each other, there seems to be some inconsistency between them. In particular in decay width. KEK; narrow FINUDA and FOPI; broad Need more experiments!

26.  Study more various K nuclei  Double K nuclei?  Other type of KN interaction? Many experiments will start, or started. T. Suzuki, Iwasaki et al; 4 He(stopped K -, n or p) @ KEK Fujioka, Nagae et al; ppK - @ DAΦNE Kishimoto et al; 16 O(inflight K -, n) 15 OK - @BNL Herrmann et al; Invariant-mass method (heavy-ion collision) @ GSI K. Suzuki et al; proton induced reaction @ GSI J-PARC I=1 p-wave KN interaction … suggested by S. Wycech et al. nucl-th/0501019 Collaborate with W. Weise  Study K nuclei from the viewpoint of quarks Collaborate with Y. Kanada-En’yo and O. Morimatsu Λ(1405) = qqq-qq, ppK - = 7qq, ppnK - = 10qq (undeca-quarks state) - --  Apply our wave function to the study of reaction Dense or not? (S. Hirenzaki and J. Yamagata) Future plans

27. Kaonic nucleus K nuclei… Exotic system ! … related to various fields!! KN interaction Cold and Dense Kaonic atom Λ （１４０５） Interesting structure … Nuclear structure Kaon condensation (Strange) Quark matter Chiral symmetry restoration