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K - 中間子原子核研究の現状

Prototype of kaonic nuclei “K - pp”. Akinobu Doté (IPNS/KEK). K - 中間子原子核研究の現状. Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN). Introduction Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological K bar N potential

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K - 中間子原子核研究の現状

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  1. Prototype of kaonic nuclei “K-pp” AkinobuDoté (IPNS/KEK) K-中間子原子核研究の現状 Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN) Introduction Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological KbarN potential Variational calculation of K-pp with a chiral SU(3)-based KbarN potential Recent status of the study of K-pp Theoretical side Experimental side Summary and future plan T. Hyodo (TITech), W. Weise (TU Munich) JAEA seminar ’10.05.13 @ JAEA, Tokai, Japan

  2. 1. Introduction

  3. 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 http://www.rarf.riken.go.jp/newcontents/contents/facility/RIBF.html

  4. 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 Strangeness ハイパー核 … J-PARC (JAEA+KEK) で展開

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

  6. p + K- p + K- 1435 1435 Λ(1405) Λ(1405) 1405 1405 Σ + π Σ + π 1325 1325 Λ + π Λ + π 1250 1250 Energy [MeV] Energy [MeV] Σ Σ 1190 1190 Λ Λ 1115 1115 I=0 Proton-K-bound state with 30MeV binding energy? Not 3 quark state? 　　←　can’t be explained with a simple quark model… 940 940 p,n p,n Actors in Kbar nuclei Leading actors Key person Excited state of Λ Supporting players

  7. p + K- 1435 Λ(1405) 1405 Σ + π 1325 Λ + π 1250 Energy [MeV] Σ 1190 Λ 1115 Σπchannel is open at about 100 MeV below the Proton-K- threshold. 940 p,n Actors in Kbar nuclei Leading actors Key person Excited state of Λ Supporting players

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

  9. Studies with a phenomenological KbarN potential • Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002) Phenomenological KbarN potential (AY KbarN potential) • free KbarNscattering data • 1s level shift of kaonic hydrogen atom • binding energy and width of Λ(1405) Strongly attractive Λ(1405) = I=0K- p quasi-bound state with 27 MeV binding energy By a calculation of a few kaonic nuclei with a simple model, 3HeK-turns out to be deeply bound by 100MeV with a narrow width of 20MeV. Deeply bound kaonic nuclei ! • A. Doté, H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004) Systematic study of various light kaonic nuclei (3HeK- to 11CK-) with AMD + G-matrix (effective NN potential ) + AY KbarN potential shows their interesting properties…

  10. ①Deeply bound and Dense ②Drastic change of structure 8Be 8BeK- ③Isovector deformation ④proton satellite pppK- Kaonic nuclei ＝ exotic system

  11. Theoretical studies of nuclear system with anti-kaons • Light nuclei with a single antikaon 3HeK-～ 11CK- studied with AMD + G-matrix + AY potential E(K)≒100MeV • Light nuclei with double antikaons 3HeK-K- etc studied with AMD + G-matrix + AY potential E(2K)≒200MeV • Medium to heavy nuclei with multi-antikaons Studied with Relativistic Mean Field • D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007); • PRC77, 045206 (2008) - T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009) … Antikaon part is based on non-linear chiralLagrangian Strongly repulsive KbarKbar interaction Saturation for the number of antikaons In case of 15O+xK-, central nuclear density and –B/x are saturated for x>8. • Nuclear matter with antikoans Neutron star, kaon condensation…

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

  13. Are kaonic nuclei really exotic? • The phenomenological KbarN potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. AY potential Chiral SU(3) KbarN πΣ ηΛ KΞ

  14. Are kaonic nuclei really exotic? • The phenomenological KbarN 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??

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

  16. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). 1E Strong repulsive core (3 GeV)

  17. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential

  18. Local KbarN potential based on Chiral SU(3) In Chiral unitary model, Resonance position in I=0 KbarN channel 1420 MeV not 1405 MeV ! T. Hyodo and W. Weise, PRC77, 035204(2008) I=0 KbarNscattering amplitude Chiral Unitary Effective potential 1420 Chiral unitary;T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003)

  19. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV • Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. Kbar N N

  20. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV • Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. × Four variants of chiral unitary modes Shallow binding and large decay width Total B. E. : 20 ± 3 MeV G（KbarN→pY） : 40 ～ 70 MeV

  21. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar N N

  22. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Cf) NN distance in normal nuclei ～ 2 fm Size of deuteron ～ 4 fm Kbar 1.97 fm N N 2.21 fm

  23. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar 1.97 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  24. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, I=0 KbarN 1.82 fm Kbar N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  25. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  26. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, “Λ(1405)” as I=0 KbarN calculated with this potential 1.86 fm I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm Kbar Almost “Λ(1405)” N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  27. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, “Λ(1405)” N Kbar Density distribution: KbarN pair in K-ppvs“L(1405)” Isospin 0 Isospin 0 KbarN pair “K-pp” N N Kbar Isospin 1 KbarN pair Isospin 0 and 1 mixed “L(1405)”almost survives in K-pp!

  28. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential B .E. Width • s-wave KbarN potential • (Variational calculation) 20 ± 3 MeV 40 ～ 70 MeV • Dispersive correction • (Effect of imaginary part) +6～ +18 MeV • p-wave KbarN potential ～ -3 MeV 10 ～ 35 MeV • Two nucleon absorption 4～ 12 MeV K-pp … Total B .E. Total Width 20 ～ 40 MeV 55 ～ 120 MeV Rough estimation Very large…

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

  30. Kbarnuclei = Exotic system !? To make the situation more clear … K-pp= Prototye of Kbar nuclei Studied with various methods, because it is a three-body system: • Doté, Hyodo, Weise Variational with a chiral SU(3)-based KbarN potential PRC79, 014003(2009) • Akaishi, Yamazaki ATMS with a phenomenological KbarN potential PRC76, 045201(2007) • Ikeda, Sato Faddeev with a chiral SU(3)-derived KbarN potential PRC76, 035203(2007) • Shevchenko, Gal , Faddeev with a phenomenological KbarN potential PRC76, 044004(2007) • Mares • Wycech, Green Variational with a phenomenological KbarN potential (with p-wave) PRC79, 014001(2009) • Arai, Yasui, OkaΛ* nuclei model PTP119, 103(2008) • continued by Uchino, Hyodo, Oka • Nishikawa, Kondo Skyrme model PRC77, 055202(2008) All calculations predict that K-pp can be bound. There are several experiments: Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN) Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti)

  31. Recent results of calculation of K-pp and related experiments Recent results of calculation of K-pp Width (KbarNN→πYN) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Akaishi, Yamazaki [2] (Variational, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) - B.E. [MeV] Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Exp. : DISTO [6] (Finalized) Exp. : FNUDA [5] Using S-wave KbarN potential constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010)

  32. Recent results of calculation of K-pp and related experiments Recent results of calculation of K-pp Width (KbarNN→πYN) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Akaishi, Yamazaki [2] (Variational, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Wycech, Green [7] (Variational, phenomenological, P-wave) - B.E. [MeV] Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Exp. : DISTO [6] (Finalized) Exp. : FNUDA [5] Using S-wave KbarN potential constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010) [7] PRC79, 014001 (2009) Including P-wave KbarN potential, and other effects.

  33. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, 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. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave KbarN potential is used.

  34. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) DHW vs AY Difference of the used KbarN interactions.

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

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

  37. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, 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=0KbarN bound state at 1420 MeV or 1405 MeV? AY potential is twice more attractive than Chiral-based one.

  38. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) DHW vs IS Although both are based on Chiral SU(3) theory, results are very different from each other. • Separable approximation? • Different energy dependence of interaction kernel Vij? • πΣNthree-body dynamics • … may not be included in DHW. (Y. Ikeda and T. Sato, PRC79, 035201(2009))

  39. Variational cal. vsFaddeev ??? Discrepancy between Variational calc. and Faddeev calc. The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory, but … Variational calculation (DHW) Faddeev calculation (IS) Total B. E. = 20±3 MeV, Decay width = 40～70 MeV Total B. E. = 60～95 MeV, Decay width = 45～80 MeV A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, 014003 (2009) Y. Ikeda, and T. Sato, Phys. Rev. C76, 035203 (2007) Why ? • Separable potential used in Faddeev calculation? • Non-relativistic (semi-relativistic) vs relativistic? • Energy dependence of two-body system (KbarN) in the three-body system (KbarNN)? • …???

  40. Variational cal. vsFaddeev ??? Discrepancy between Variational calc. and Faddeev calc. The KbarN potentials used in both calculations are constrained with Chiral SU(3) theory, but … Three-body system calculated with the effective KbarN potential In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective KbarN potential. Variational calculation (DHW) Faddeev calculation (IS) π π K K K … K = + … N N N N Σ Σ Total B. E. = 20±3 MeV, Decay width = 40～70 MeV Total B. E. = 60～95 MeV, Decay width = 45～80 MeV conserved N N N N N N A. Doté, T. Hyodo and W. Weise, Phys. Rev. C79, 014003 (2009) Y. Ikeda, and T. Sato, Phys. Rev. C76, 035203 (2007) A possible reason is Y. Ikeda and T. Sato, PRC79, 035201(2009) πΣN thee-body dynamics

  41. Experiments related to K-pp

  42. If it is K-pp, … Total binding energy = 115 MeV Decay width = 67 MeV PRL 94, 212303 (2005) Strong correlation between emitted p and Λ(back-to-back) Invariant mass of p and Λ Experiments related to K-pp • FINUDA collaboration (DAΦNE, Frascatti) • K- absorption at rest on various nuclei (6Li, 7Li, 12C, 27Al, 51V) • Invariant-mass method p p K- p Λ

  43. Experiments related to K-pp • Re-analysis of KEK-PS E549 • K- stopped on 4He target • Λp invariant mass Strong Λp back-to-back correlation is confirmed. Unknown strength is there in the same energy region as FINUDA. T. Suzuki et al (KEK-PS E549 collaboration), arXiv:0711.4943v1[nucl-ex] • DISTO collaboration • p + p -> K+ + Λ + p@ 2.85GeV • Λp invariant mass • Comparison with simulation data K- pp??? B. E.= 103 ±3 ±5 MeV Γ = 118 ±8 ±10 MeV T. Yamazaki et al. (DISTIO collaboration), PRL104, 132502 (2010)

  44. J-PARC will give us lots of interesting data! Dr. Fujioka’s talk (KEK workshop, 7-9. Aug. 08) E15: A search for deeply bound kaonic nuclear states by 3He(inflightK-, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) E17: Precision spectroscopy of kaonic3He atom 3d→2pX-rays --- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken) All emitted particles will be measured.

  45. 4. Summary and future plan

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

  47. 4. Summary Current status of studies of K-pp The most essential Kbar nuclei “K-pp” (KbarNN, Jp=1/2-, T=0) has been investigated in various ways. But the situation is still controversial… Theory Variational + Phenom. KbarNB.E. = 47MeV, Γ= 61MeV PRC76, 045201(2007) Variational + Chiral-based KbarN B.E. = 20±3MeV, Γ= 40～70MeV PRC79, 014003(2009) Faddeev + Phenom. KbarN B.E. = 50～70MeV, Γ=～100MeV PRC76, 044004(2007) Faddeev + Chiral-based KbarN B.E. = 60～95MeV, Γ= 45～80MeV PRC76, 035203(2007) … if it is K-pp Experiment (Unknown object which seems related to K-pp) FINUDA B.E. = 115MeV, Γ= 67MeV PRL94, 212303(2005) DISTO B.E. = 103MeV, Γ= 118MeV PRL104, 132502 (2010) Discrepancy between theoretical studies of K-pp • DHW (Variational with Chiral-based) vs AY (Variational with phenomenological) • … Difference of KbarN 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? )

  48. 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 πΣNdegree 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???) Coupled channel Complex Scaling Direct treatment of πΣN degree, dealing with a resonant state, based on variational scheme.

  49. Thank you for your attention!

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