1. Unique Feature and Perspectives of Nuclear K Bound Systems K-K- Atomic states Nuclear state Chiral05 Feb. 17, 2005 Yoshinori AKAISHI, Akinobu DOTE and Toshimitsu YAMAZAKI _

2. Few-Body KN Systems _ Strange baryon Di-baryon Tri-baryon Tetra-baryon Strange heavy nucleus Strange matter pp p p p n n p p n p p n S=-1 S=-2 p  K _ = p p   = H*? DA  NE1999 Y. Akaishi & T. Yamazaki Kaplan-Nelson Brown-Rho

3. DEAR @ DA  NE K  X-ray 1S 2P

4. KN interaction - -62 MeV -285 MeV -436 MeV -412 MeV none KpX Iwasaki et al. (1997) Martin (1981) p+K - n+K 0 -  (1405) -++-++ ++-++- 0+00+0 +0+0 5.3 0 -27 -94.9 -103.0 -104.4 -181.3 (MeV)

5. L.Ya. Glozman, W. Plessas, K. Varga & R.F. Wagenbrunn, Phys. Rev. D 58 (1998) 094030. A Chiral Constituent-Quark Model Lattice QCD quenched to 3Q H. Suganuma et al. Theor Exp N  1.8 1.6 1.4 1.2 1.0 GeV 1.8 1.6 1.4 1.2 1.0 GeV  (1405) Exp Theor  (1385) 

6. no  (1670) Funabashi potential : M. Wada, M. Obu, S. Shinmura

7. Chiral SU(3) Dynamics T. Waas, N. Kaiser & W. Weise, Phys. Lett. B379 (1996) 34. 0123 1.5 1.0 0.5 0.0 K+K+ K-K- 200 MeV  /100 MeV Tomozawa-Weinberg 7 times Chiral symmetry NN KN - Isoscalar

8. Nuclear KNN bound states _ T = 3/2 Unbound T = 1/2 Above the  + n threshold T = 1/2 E = -48 MeV  = 61 MeV S = 0 S = 1 S = 0 obtained from 3-body variational calculation V T=0

9. Structure of ppK - pp K-K- 1.90 fm rms distance 1.36 fm 0.8 0.6 0.4 0.2 0.0 fm -3 02468 r fm 3.90 fm rms distance T. Yamazaki & Y. Akaishi, Phys. Lett. B535 (2002) 70.

10. K - + p 123 r fm 0 -50 -200 -300 -400 -500 MeV  (1405) ++ ++ K - + pp 123 r fm 0 -50 -200 -300 -400 -500 MeV ++ ++ K - + 3 He 123 r fm 0 -50 -200 -300 -400 -500 MeV ++ ++

11. J.K. Ahn, Nucl. Phys. A721 (2003) 715c J.C. Nacher, E. Oset, H. Toki & A. Ramos, Phys. Lett. B455 (1999) 55. M.F.M. Lutz & E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193. 1.31 fm p

12.    KN   Chiral dynamics of two  (1405) states D. Jido, J.A. Oller, E. Oset, A. Ramos & U.-G. Meissner, Nucl. Phys. A 725 (2003) 181 Experimental check !

13. pp T. Yamazaki & Y. Akaishi, Phys. Lett. B535 (2002) 70.  (1405) Doorway State

14. 123 r fm 0 -100 -200 -300 -400 MeV ++ (-69, 66) MeV (-86, 32) MeV Nuclear bound state 1.47 fm Free 1.01.21.41.6 1.01.21.41.6 R core fm 40 30 20 10 0 -60 -70 -80 -90 -100 -110 -120 MeV  E core (R core ) E K (R core ) E K +  E core Hasegawa-Nagata’s NN ~1Gev repulsion E  Y. Akaishi & T. Yamazaki, Phys. Rev. C 65 (2002) 044005 Shrinkage !

15. 0 -50 -100 -150 50 70 90 15 MeV T n MeV ４ He ( stopped K -, n) Branching ~2% M. Iwasaki et al., Nucl. Inst. Meth. A473 (2001) 286. K - + 3 He T = 1 T = 0 -108 MeV E K MeV d+  - +   d+  + +   d+  - +  

16. Evidence for K - ppn Oct.16, 2003 M. Iwasaki et al. M. Iwasaki T. Suzuki H. Bhang G. Franklin K. Gomikawa R.S. Hayano T. Hayashi K. Ishikawa S. Ishimoto K. Itahashi T. Katayama Y. Kondo Y. Matsuda T. Nakamura S. Okada H. Outa B. Quinn M. Sato M. Shindo H. So T. Sugimoto P. Strasser K. Suzuki S. Suzuki D. Tomono A.M. Vinodkumar E. Widmann T. Yamazaki T. Yoneyama nucl-ex/0310018 from 4 He(stopped K -,n)

17. ppnK - udd uud us _ 11 or 9 quarks ? What structure? Challenging problem ! Meson-baryon ? pp n K-K- 1.5 fm  N (0) = 8.9  0   av =3.1  0 Y. En’yo et al.,  + 1.2 fm Exp.  B ｔｈ -ex ~ 60 MeV Chiral restoration ? Relativistic effect ? m K / f 2

18. Atomic systems by point-Coulomb interaction 0 -100 -200 -300 -400 -500 [MeV] 20406080100120140 Z Schroedinger Dirac Klein-Gordon Z  =1 -mc 2 =-494 MeV m X

19. Klein-Gordon equation Atomic state Deeply bound state

20. K - -p  (1405) K - -ppn S 1 (3140)   V 0  s  -581 -27.0 Sch -581 unbound K-G(s) -581 -71.1 -81.3 K-G(v) -446 -4.0 Sch -446 -25.9 -27.1 K-G(v) [MeV] Mapping

21. SS Relativistic effect Kaon condensation   RC 0 -100 -200 -300 -400 -500 (MeV) 0 -100 -200  T RC  RC (MeV) (Virial)

22. 0 -100 -200 -300 -400 -500 -600 [MeV] 12 r [fm] 100 -161 Separation energy Binding energy “Separating” pot. “Binding” pot. 50 _ _ _ -34 -211 (Effective KN int. with enhancement by 9%) Bare KN int. with enhancement by 15 % 0 -100 -200 -300 -400 -500 -600 [MeV] 1 23 r [fm] -5 [MeV] -23 Relativistic effect -176 -83 -153 100 UK(r)UK(r) Without shrinkage With shrinkage Bare KN int. without enhancement Core polarization due to shrinkage r Core Exp. -169+8 = -161

23. A. Dote et al., Phys. Rev. C70 (2004) 044313 NN LS potential effect 3 P 2 pairing N(0s) 2 (0p) K _ N(0s) 3 K _ T=1 T=0 T=1 T=0 T=1 T=0 T=2

24. Observe all. Exciting ! pppK - ppnK - pnnK - -111 MeV N(0s) 3 K N(0s) 2 (0p) K -97 MeV -135 MeV -126 MeV Bare KN interaction enhanced by 15% _ _ _ -194 MeV( obs.) 3/2 + T=1 1/2 + T 3 =1 T 3 =0 T 3 =-1 Relativistic effect -169 MeV (obs.) T=0,1/2 -

25. T. Suzuki H. Bhang G. Franklin K. Gomikawa R.S. Hayano T. Hayashi K. Ishikawa S. Ishimoto K. Itahashi M. Iwasaki T. Katayama Y. Kondo Y. Matsuda T. Nakamura S. Okada H. Outa B. Quinn M. Sato M. Shindo H. So P. Strasser T. Sugimoto K. Suzuki S. Suzuki D. Tomono A.M. Vinodkumar E. Widmann T. Yamazaki T. Yoneyama Discovery of S 0 (3115) in 4 He(stopped K -,p)K - pnn Phys. Lett. B597 (2004) 263 Press release on Aug. 24, 2004 13 

26. 4 He( stopped K -, n) 4 He( stopped K -, p) S 0 (3115)? S 1 (3140)? S 0 (3115) -194 MeV( obs.) 3/2 + T=1 1/2 + T=0,1/2 -

27. Spectra from (  +,K + ) Reaction P  =1.5 GeV/c Green’s function method O. Morimatsu & K. Yazaki, Nucl. Phys. A435 (1985) 727

28. Relativistic effect SS Kaon condensation   RC 0 -100 -200 -300 -400 -500 [MeV] 0 -100 -200 [MeV] ppn-K - pnn-K - T=0 1/2 - T=1 3/2 +

29. Nona-Quark States Y. Maezawa, T. Hatsuda & S. Sasaki, Hep-ph/0412025 Color-magnetic interaction MIT bag: R 9 =1.3 fm S 1 (3140) S 0 (3115) Search !

30. ppnK - pp n K-K- 1.50 fm  N (0) = 8.9  0   av =3.1  0 1.19 fm 9-quark ? or 11-quark ? (kaonic nucl.) 1.31 fm p  (1405) 3-quark ? or 5-quark ?

31. Nucleon density distribution ppnK - pppK - pppnK - 6 BeK - 3 fm 9 BK - 4 fm

32. pppnK - pppK - ppK - Spectral Function  * Q.F. 500 300 400 600 700 0 2 4 6 400450 350 Arbitrary unit

33. 8 Be 8 BeK - 7 fm Density (/fm^3) 0.0 0.41 0.83 Density (/fm^3) 0.0 0.10 0.20 A ntisymmetrized M olecular D ynamics calculation A. Dote, H. Horiuchi, Y. Akaishi & T. Yamazaki, Phys. Lett. B590 (2004) 51. Dense & Cold

34. T. Hatsuda & T. Kunihiro, Phys. Rev. Lett. 55 (1985) 158. M. Lutz, S. Klimt & W. Weise, Nucl. Phys. A542 (1992) 52. W. Weise, Nucl. Phys. A553 (1993) 59c. 300 MeV 5050 Temperature T Density  Normal density

35. Color forromag. A. Iwazaki, O. Morimatsu et al. 150 MeV Chemical potential Nuclei Temperature Quark-gluon plasma Color superconductor (2SC), (CFL) Hadrons Dense & cold Tricritical point Nuclear Phase Diagram Liquid-gas

37. 1.90 fm 1.36 fm pp ppK - 1.3 fm 1.5 fm ppK - K - uuddss us _ uud us _ Strange deuteron? Excited H* di-baryon? K-K- K-K- T. Yamazaki P. Kienle

38. ppnK -  + d K-K- Cold & dense fragments Heavy-Ion Reaction ~10A GeV High-density environment provided by HI fireball Invariant-mass spectroscopy for their decays “Decay-channel spectroscopy” T. Yamazaki Phys. Lett. B587 (2004) 167 ppK -  + p

39. Concluding Remarks Nuclear K bound state _ Mini strange matter K plays a role of “contractor”. _ Few-body K nuclear systems would provide experimental data of fundamental importance for hadron physics with strangeness. _ A new means to investigate hadron dynamics in dense&cold matter Chiral restoration? Color superconductivity? Kaon condensation? Strange hadronic/quark matter? Production-/Decay- channel spectroscopies KEK DA  NE SPring-8 GSI J-PARC Missing-mass/Invariant-mass  /J

40. S=0 nucleiS=-1S=-2 500 400 300 200 100 0 Excitation energy (MeV) Nuclei of 2 nd generation The s quark plays a leading role in forming a dense and cold nucleus. A new paradigm of Nuclear Physics T. Yamazaki et al. An epoch-making milestone has been obtained by T. Suzuki, M. Iwasaki et al.